understand the concept behind reaching the formula. What ... · PDF fileMail your comments and...
1
-¨¡-E-¢√®Ωç 12 -ÅéÓd-•®Ω’ 2013 Ñ-Ø√-úø’ £j«-ü¿®√-¶«-ü˛ 1 1. The area of a rectangular plate is 236.25 sq.cm. If the length of the plate is 17.5 cm, find the perimeter of the plate. 1) 65 cm 2) 52 cm 3) 62 cm 4) 67 cm 5) None of these 2. The breadth of a rectangular plot is 75% of its length. If the perimeter of the plot be 1050 m, what is its area? 1) 12500 2) 57500 3) 62500 4) 67500 5) None of these 3. In measuring the sides of a rectangle, one side is taken 10% in excess, and the other 5% in deficit. What is the change in its area as a percentage? 1) 1.5% 2) 4.5% 3) 2.5% 4) 5% 5) None of these 4. How many tiles of 20 cm length and 10 cm width are required to pave the floor of a room 8 m long and 5 m wide? 1) 2100 2) 1500 3) 2500 4) 2000 5) None of these 5. The circumference of two circles is 88 metre and 132 metre respectively. What is the dif- ference between the area of the larger circle and the smaller circle? 1) 440 sq.m 2) 510 sq.m 3) 770 sq.m 4) 225 sq.m 5) None of these 6. A solid metallic spherical ball of radius 7 cm is melted down and recast into small cones. If the diameter of the base of the cone is 14 cm and the height is 2 cm, find the num- ber of such cones can be made. 1) 14 2) 28 3) 7 4) 12 5) None of these 7. A hall is 10metres long and 8metres wide. What will be the cost of carpeting the room if 0.5 metres of space is left around the room? The rate of 0.25 metre wide carpet is Rs.20 per metre. 1) Rs.1560 2) Rs.2520 3) Rs.1875 4) Rs.5040 5) None of these 8. A square field has an area of 50625 sq. m. Find the cost of fencing around it at Rs. 15 per metre. 1) Rs.12500 2) Rs.17500 3) Rs.13500 4) Rs.16250 5) None of these 9. Cost of fencing a circular plot at the rate of Rs.12 per metre is Rs.2,640. What will be the cost of carpeting the floor of the plot at the rate of Rs.85 per square metre? 1) Rs.3,25,250 2) Rs.3,22,350 3) Rs.3,27,250 4) Rs.3,25,750 5) None of these 10. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What will be the area of the circle? 1) 88 cm 2 2) 1250 cm 2 3) 154 cm 2 4) 128 cm 2 5) None of these 11. A circular garden has a 7 m wide road around the border. Find the cost of leveling the road at Rs.5 per square meter if the radius of the inner circle is 21 m? 1) Rs.3490 2) Rs.5390 3) Rs.2930 4) Rs.5695 5) None of these 12. The lateral surface area of a cylinder is thrice the area of its base. Find the ratio of its height and the base radius? 1) 2:3 2) 2:5 3) 3:2 4) 4:9 5) None of these 13. Two cubes have their volumes in the ratio 8:27. Find the ratio of their surface areas. 1) 2:3 2) 4:9 3) 16:81 4) 8:9 5) None of these 14. A horse is tied with a 14 m long rope. How much ground will it be able to graze? 1) 125 Sq.m 2) 275 Sq.m 3) 625 Sq.m 4) 675 Sq.m 5) None of these 15. Find the length of the longest stick that can be placed in a room of 12 m long, 9 m broad and 8 m high. 1) 21 m 2) 29 m 3) 20 m 4) 17 m 5) None of these 16. A field is 375 m long and 40 m broad. A tank 30 m long, 20 m broad and 12 m deep is dug in the field and earth taken out of it and is spread equally over the field. How much is the level of field raised? 1) 48 cm 2) 0.5 cm 3) 25 cm 4) 50 cm 5) None of these 17. A rectangular field of 60-metre length and 40 metres wide is to be surrounded by a road 5 meter wide. If the cost of making 1 square meter road is Rs.500, what would be the cost of the entire road? 1) Rs.6,25,000 2) Rs.5,55,000 3) Rs.5,50,000 4) Rs.5,67,500 5) None of these 18. A room is 7.5 m long, 5.5 m broad and 5 m high. What will be the expenditure in cover- ing the walls by paper 40 cm broad at the rate of 75 paise per meter? 1) Rs.245.25 2) Rs.243.75 3) Rs.275.50 4) Rs.275.45 5) None of these 19. The length and breadth of a rectangle increased by 20% and 10% respectively. How much percent will its area be increased? 1) 25% 2) 30% 3) 40% 4) 32% 5) None of these 20. 7 cm radius and 28 cm height solid metallic cylinder is melted and recast into small spherical balls of 7cm radius. Find the num- ber of cubes that can be made. 1) 12 2) 5 3) 3 4) 6 5) None of these What will be the area of the circle? (Writer − Director, RACE Institute, Hyderabad) 1-3 2-4 3-2 4-4 5-3 6-1 7-4 8-3 9-3 10-5 11-2 12-3 13-2 14-5 15-4 16-4 17-3 18-2 19-4 20-3 ANSWERS Mensuration means measurement. It is being done in our life in many situations. For example, Length of cloth we need for stitching, the area of a wall which is being painted, perimeter of a rectangular plot to be fenced, quantity of water needed to fill the tank etc. For these kinds of activities, we are doing measurements for further needs. EXPLANATIONS 236.251 1. Width of the plate = ⎯⎯⎯⎯⎯ = 13.5 cm 17.5 Perimeter = 2 (length + width) ⇒ 2 (17.5 + 13.5) = 62 cm. 2. Let the length of the plot be x m 75 3x ∴ Breadth = ⎯⎯ × x = ⎯ m 100 4 Perimeter = 1050. ∴ 1050 = 2 (x + 3x ⎯ 4 ) ∴ x = 300 m. ∴ Area of the plot 3 × 300 = 300 × ⎯⎯⎯ 4 = 67500 m 2 3. Let the length be 10 and breadth also be 10. ∴ Area = 10 × 10 = 100 New length (10% excess) = 11, New breadth (5% deficit) = 9.5 New area = 11 × 9.5 = 104.5 ∴ Change in area = 104.5 − 100 = 4.5 4.5 Percentage change = ⎯⎯ × 100 100 = 4.5% 4. Area of the floor of the room = 800 × 500 = 400000 cm 2 Area of the Tile = 20 ×10 cm 2 400000 ∴ Number of Tiles required = ⎯⎯⎯⎯ 20 × 10 = 2000 5. Let the radius of larger circle be 'R' and smaller circle be 'r' ∴ 2 π R = 132 ⇒ 2 × 22 ⎯ 7 × R = 132 ⇒ R = 21 2πr = 88 ⇒ 2 × 22 ⎯ 7 × r = 88 ⇒ r = 14 Difference in the areas = π R 2 − π r 2 = π ( R 2 − r 2 ) ⇒ 22 ⎯ 7 (21 2 − 14 2 ) ⇒ 22 ⎯ 7 (21 + 14) (21 − 14) ⇒ 22 ⎯ 7 × 35 × 7 = 770 sq.metres 6. Volume of sphere = b 4 ⎯ 3 πr 3 Volume of cone = 1 ⎯ 3 πr 2 h Let the number of cones be 'x' ∴ 4 ⎯ 3 πr 3 = 1 ⎯ 3 πr 2 h × x ⇒ 4 ⎯ 3 π × 7 3 = 1 ⎯ 3 π × 7 2 × 2 × x ⇒ x = 14 7. Length of the carpet = 10 − (0.5 + 0.5) = 9 m Width of the carpet = 8 − (0.5 + 0.5) = 7 m Area of carpet = 9 × 7 = 63 63 Required length of carpet = ⎯⎯ = 252 m 0.25 ∴Cost of carpet = 252 × Rs.20 = Rs.5,040. ⎯⎯⎯ 8. Side of the square field = √ 50625 = 225 m Length of the wire required = 4 × 225 = 900 m ∴Total cost = Rs.15 × 900 = Rs.13,500 9. Circumference of the circular plot 2640 = ⎯⎯⎯ = 220 m 12 2πr = 220 ⇒ 2× 22 ⎯ 7 × r = 220 ⇒ r = 35 m Area of the plot = πr 2 = 22 ⎯ 7 × 35 × 35 = 3850 sq.m ∴ Cost of carpeting = 3850 × Rs.85 = Rs.3,27,250 10. Perimeter of rectangle = 2(18 + 26) = 88 cm Circumference of circle 2πr = 88 ⇒ 2 × 22 ⎯ 7 × r = 88 ⇒ r = 14 cm Area of circle = πr 2 = 22 ⎯ 7 × 14 × 14 = 616 cm 2 11. Radius of outer circle = 21 + 7 = 28 m Road area = Area of outside circle − Area of inside circle Road area = π(28) 2 −π(21) 2 = 1078 sq.m ∴Cost = 1078 × Rs.5 = Rs.5,390. 12. Lateral surface area of cylinder = 2πrh Base area of cylinder = πr 2 ∴ 2πrh = 3πr 2 ⇒ h: r = 3 : 2 13. Let the sides of two cubes be a 1 and a 2 a 1 3 : a 2 3 = 8:27 ⇒ a 1 : a 2 = 2:3 ∴ Surface areas ratio = 6a 1 2 : 6a 2 2 = (2) 2 : (3) 2 = 4:9 14. Length of the rope will be the radius of the circle = 14 m Area of the circle = πr 2 = 22 ⎯ 7 × 14 × 14 = 616 sq.m ∴ Area of the ground that can be grazed = 616 sq.m. 15. Length of the stick = length of the diagonal of the room ⎯⎯⎯⎯⎯ ⎯⎯ √ 12 2 + 9 2 + 8 2 = √ 289 = 17 m 16. Quantity of the earth taken from the tank = 30 × 20 × 12 cu.m Area of the field for the earth to be spreaded = (375 × 40) − (30 × 20) = 14400 ∴ The rise in the level of the field 30 × 20 × 12 = ⎯⎯⎯⎯⎯ × 100 = 50 cm 14400 17. Area of the road = Area of outside rectangle − Area of inside rectangle = 70 × 50 − 60 × 40 = 3500 − 2400 = 1100 m 2 ∴ The cost of making 1100 m 2 = 500 × 1100 = Rs.5,50,000 18. Area of four walls = 2 × 5 (7.5 + 5.5) = 130 m 2 Area of required paper = 130 m 2 Breadth of the paper = 40 cm = 0.4 m 130 ∴ Length of the paper = ⎯⎯ = 325 m 0.4 ∴ Cost of paper at 75 paise per meter = 325 × 0.75 = Rs.243.75 19. Let the length and breadth be 10 and 10 Area = 10 × 10 = 100 New length = 12 (20% increase) New breadth = 11 (10% increase) New area = 12 × 11 = 132 ∴ Increment in area = 132 − 100 = 32%. 20. Let the number of spherical balls be 'x' Volume of cylinder = x × Volume of sphere π × 7 2 × 28 = x × 4 ⎯ 3 × π × 7 3 x = 3 Quantitative Aptitude G.S. Giridhar [email protected] Mail your comments and suggestions to Here, we cover three areas 1. Perimeter 2. Area 3. Volume To find these things we have to remember the formulae of plane figures and solid figures. Try to understand the concept behind reaching the formula. MENSURATION
Transcript of understand the concept behind reaching the formula. What ... · PDF fileMail your comments and...
-¨¡-E-¢√®Ωç 12 -ÅéÓd-•®Ω’ 2013 Ñ-Ø√-úø’ £j«-ü¿®√-¶«-ü˛ 1
1. The area of a rectangular plate is 236.25sq.cm. If the length of the plate is 17.5 cm,find the perimeter of the plate. 1) 65 cm 2) 52 cm 3) 62 cm 4) 67 cm 5) None of these
2. The breadth of a rectangular plot is 75% ofits length. If the perimeter of the plot be 1050 m, what is its area? 1) 12500 2) 57500 3) 62500 4) 67500 5) None of these
3. In measuring the sides of a rectangle, oneside is taken 10% in excess, and the other5% in deficit. What is the change in its areaas a percentage? 1) 1.5% 2) 4.5% 3) 2.5% 4) 5% 5) None of these
4. How many tiles of 20 cm length and 10 cmwidth are required to pave the floor of a room8 m long and 5 m wide? 1) 2100 2) 1500 3) 2500 4) 2000 5) None of these
5. The circumference of two circles is 88 metreand 132 metre respectively. What is the dif-ference between the area of the larger circleand the smaller circle? 1) 440 sq.m 2) 510 sq.m 3) 770 sq.m 4) 225 sq.m 5) None of these
6. A solid metallic spherical ball of radius 7 cmis melted down and recast into small cones.If the diameter of the base of the cone is 14 cm and the height is 2 cm, find the num-ber of such cones can be made. 1) 14 2) 28 3) 7 4) 12 5) None of these
7. A hall is 10metres long and 8metres wide.What will be the cost of carpeting the room if0.5 metres of space is left around the room?The rate of 0.25 metre wide carpet is Rs.20per metre. 1) Rs.1560 2) Rs.2520 3) Rs.1875 4) Rs.5040 5) None of these
8. A square field has an area of 50625 sq. m.Find the cost of fencing around it at Rs. 15per metre. 1) Rs.12500 2) Rs.17500 3) Rs.13500 4) Rs.16250 5) None of these
9. Cost of fencing a circular plot at the rate ofRs.12 per metre is Rs.2,640. What will bethe cost of carpeting the floor of the plot atthe rate of Rs.85 per square metre? 1) Rs.3,25,250 2) Rs.3,22,350 3) Rs.3,27,250 4) Rs.3,25,750 5) None of these
10. A circle and a rectangle have the sameperimeter. The sides of the rectangle are 18 cm and 26 cm. What will be the area ofthe circle? 1) 88 cm2 2) 1250 cm2
3) 154 cm2 4) 128 cm2
5) None of these 11. A circular garden has a 7 m wide road
around the border. Find the cost of levelingthe road at Rs.5 per square meter if theradius of the inner circle is 21 m? 1) Rs.3490 2) Rs.5390 3) Rs.2930 4) Rs.5695 5) None of these
12. The lateral surface area of a cylinder isthrice the area of its base. Find the ratio ofits height and the base radius?
1) 2:3 2) 2:5 3) 3:2
4) 4:9 5) None of these
13. Two cubes have their volumes in the ratio8:27. Find the ratio of their surface areas.
1) 2:3 2) 4:9 3) 16:81
4) 8:9 5) None of these
14. A horse is tied with a 14 m long rope. Howmuch ground will it be able to graze?
1) 125 Sq.m
2) 275 Sq.m
3) 625 Sq.m 4) 675 Sq.m
5) None of these
15. Find the length of thelongest stick that can beplaced in a room of 12 m long, 9m broad and 8 m high.
1) 21 m 2) 29 m
3) 20 m 4) 17 m
5) None of these
16. A field is 375 m long and 40 mbroad. A tank 30 m long, 20 mbroad and 12 m deep is dug inthe field and earth taken out of it and isspread equally over the field. How much isthe level of field raised?
1) 48 cm 2) 0.5 cm 3) 25 cm
4) 50 cm 5) None of these
17. A rectangular field of 60-metre length and40 metres wide is to be surrounded by aroad 5 meter wide. If the cost of making 1square meter road is Rs.500, what wouldbe the cost of the entire road?
1) Rs.6,25,000 2) Rs.5,55,000
3) Rs.5,50,000 4) Rs.5,67,500
5) None of these
18. A room is 7.5 m long, 5.5 m broad and 5 mhigh. What will be the expenditure in cover-ing the walls by paper 40 cm broad at therate of 75 paise per meter?
1) Rs.245.25 2) Rs.243.75
3) Rs.275.50 4) Rs.275.45
5) None of these
19. The length and breadth of a rectangleincreased by 20% and 10% respectively.How much percent will its area beincreased?
1) 25% 2) 30% 3) 40%
4) 32% 5) None of these
20. 7 cm radius and 28 cm height solid metalliccylinder is melted and recast into smallspherical balls of 7cm radius. Find the num-ber of cubes that can be made.
1) 12 2) 5 3) 3
4) 6 5) None of these
What will be the area of the circle?
(Writer − Director, RACE Institute, Hyderabad)
1-3 2-4 3-2 4-4
5-3 6-1 7-4 8-3
9-3 10-5 11-212-3
13-214-515-416-4
17-318-219-420-3
ANSWERS
Mensuration means measurement. It is being done in our life inmany situations. For example, Length of cloth we need for
stitching, the area of a wall which is being painted, perimeter ofa rectangular plot to be fenced, quantity of water needed to fill
the tank etc. For these kinds of activities, we are doing measurements for further needs.
EXPLANATIONS236.251
1. Width of the plate = ⎯⎯⎯⎯⎯ = 13.5 cm17.5
Perimeter = 2 (length + width)⇒ 2 (17.5 + 13.5) = 62 cm.
2. Let the length of the plot be x m 75 3x
∴ Breadth = ⎯⎯ × x = ⎯ m 100 4
Perimeter = 1050.
∴ 1050 = 2 (x + 3x⎯4
)∴ x = 300 m.∴ Area of the plot
3 × 300= 300 × ⎯⎯⎯
4
= 67500 m2
3. Let the length be 10 andbreadth also be 10.
∴ Area = 10 × 10 = 100 New length (10% excess) = 11, New breadth (5% deficit) = 9.5 New area = 11 × 9.5 = 104.5∴ Change in area = 104.5 − 100
= 4.54.5
Percentage change = ⎯⎯ × 100 100
= 4.5%4. Area of the floor of the room = 800 × 500
= 400000 cm2
Area of the Tile = 20 ×10 cm2
400000 ∴ Number of Tiles required = ⎯⎯⎯⎯
20 × 10= 2000
5. Let the radius of larger circle be 'R' andsmaller circle be 'r'
∴ 2 πR = 132 ⇒ 2 ×22⎯7
× R = 132 ⇒ R = 21
2πr = 88 ⇒ 2 ×22⎯7
× r = 88 ⇒ r = 14
Difference in the areas = π R2 − π r2
= π (R2− r2)⇒
22⎯7
(212 − 142) ⇒ 22⎯7
(21 + 14) (21 − 14)
⇒22⎯7
× 35 × 7 = 770 sq.metres
6. Volume of sphere = b4⎯3
πr3
Volume of cone = 1⎯3
πr2h
Let the number of cones be 'x'
∴ 4⎯3
πr3 = 1⎯3
πr2h × x
⇒ 4⎯3
π × 73 = 1⎯3
π × 72 × 2 × x
⇒ x = 14 7. Length of the carpet = 10 − (0.5 + 0.5) = 9 m
Width of the carpet = 8 − (0.5 + 0.5) = 7 mArea of carpet = 9 × 7 = 63
63Required length of carpet = ⎯⎯ = 252 m
0.25∴Cost of carpet = 252 × Rs.20 = Rs.5,040.
⎯⎯⎯8. Side of the square field = √ 50625 = 225 m
Length of the wire required = 4 × 225 = 900 m
∴Total cost = Rs.15 × 900 = Rs.13,5009. Circumference of the circular plot
2640= ⎯⎯⎯ = 220 m
12
2πr = 220 ⇒ 2× 22⎯7
× r = 220 ⇒ r = 35 mArea of the plot
= πr2 =22⎯7
× 35 × 35 = 3850 sq.m
∴ Cost of carpeting = 3850 × Rs.85= Rs.3,27,250
10. Perimeter of rectangle = 2(18 + 26) = 88 cmCircumference of circle 2πr = 88
⇒ 2 × 22⎯7
× r = 88 ⇒ r = 14 cm
Area of circle = πr2 = 22⎯7
× 14 × 14
= 616 cm2
11. Radius of outer circle = 21 + 7 = 28 mRoad area = Area of outside circle − Area of
inside circleRoad area = π(28)2 − π(21)2 = 1078 sq.m ∴Cost = 1078 × Rs.5 = Rs.5,390.
12. Lateral surface area of cylinder = 2πrhBase area of cylinder = πr2
∴ 2πrh = 3πr2
⇒ h: r = 3 : 213. Let the sides of two cubes be a1 and a2
a13 : a
23 = 8:27 ⇒ a1: a2 = 2:3
∴ Surface areas ratio = 6a12 : 6a2
2
= (2)2 : (3)2 = 4:914. Length of the rope will be the radius of the
circle = 14 mArea of the circle
= πr2 = 22⎯7
× 14 × 14 = 616 sq.m
∴ Area of the ground that can be grazed= 616 sq.m.
15. Length of the stick = length of the diagonalof the room
⎯⎯⎯⎯⎯ ⎯⎯√ 122 + 92 + 82 = √ 289 = 17 m
16. Quantity of the earth taken from the tank = 30 × 20 × 12 cu.m
Area of the field for the earth to be spreaded= (375 × 40) − (30 × 20) = 14400∴ The rise in the level of the field
30 × 20 × 12= ⎯⎯⎯⎯⎯ × 100 = 50 cm
1440017. Area of the road
= Area of outside rectangle − Area of insiderectangle
= 70 × 50 − 60 × 40= 3500 − 2400 = 1100 m2
∴ The cost of making 1100 m2
= 500 × 1100 = Rs.5,50,00018. Area of four walls = 2 × 5 (7.5 + 5.5)
= 130 m2
Area of required paper = 130 m2
Breadth of the paper = 40 cm = 0.4 m
130∴ Length of the paper = ⎯⎯ = 325 m
0.4
∴ Cost of paper at 75 paise per meter
= 325 × 0.75 = Rs.243.7519. Let the length and breadth be 10 and 10
Area = 10 × 10 = 100New length = 12 (20% increase)New breadth = 11 (10% increase)New area = 12 × 11 = 132
∴ Increment in area = 132 − 100 = 32%.
20. Let the number of spherical balls be 'x'Volume of cylinder = x × Volume of sphere
π × 72 × 28 = x × 4⎯3
× π × 73
x = 3
Quantitative Aptitude
G.S. Giridhar
[email protected] your comments and suggestions to
HHere, we cover three areas
1. Perimeter 2. Area 3. Volume
To find these things we have toremember the formulae of plane figures and solid figures. Try tounderstand the concept behindreaching the formula.
MENSURATION
![Isoperimetric Polygons of Maximum Width · pus [23] and Theon of Alexandria [11]. The solution is the set of regular polygons. Since Reinhardt’s [20] ... i=1 ci denotes the perimeter](https://static.fdocument.org/doc/165x107/5aeb3f837f8b9a3b2e8db8f4/isoperimetric-polygons-of-maximum-width-23-and-theon-of-alexandria-11-the-solution.jpg)
![1BDJGJD +PVSOBM PG .BUIFNBUJDT - MSP · abelian groups [6] in 1937, many attempts have been made to give structure theorems for classes of torsion-free abelian groups reaching beyond](https://static.fdocument.org/doc/165x107/60f7aaba7069f719c90d5ee2/1bdjgjd-pvsobm-pg-buifnbujdt-msp-abelian-groups-6-in-1937-many-attempts-have.jpg)
