Otba Maths

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  • OTBA Maths SA II THEME 2 Q1) If canvas is used to make a cylindrical tent of radius of base 7 m., then what should be the volume of air inside the tent? Answer Surface area of cylindrical tent = 551 - 1m2 = 2rh + r2 Or, 550 = 2 7 h + 7 7 Or, 550-15422277=h h = 9 m Volume of cylinder = r2h r2h = (22/7) 7 7 9 = 1386 m3 Q2) The survey conducted by Sarah on the success rate of the team members of Brigadier Tripathi Team climbing the rock is represented in the form of a bar graph as shown below.

    Observe the bar graph and answer the following questions. a. In how many attempts do most of the team members who tried climbing the rock climbed the rock and what is their number? b. How many team members climbed the rock? c. How many team members climbed the rock in not more than two attempts? Answer

  • From the bar graph, we can see that a. Most of the team members climbed the rock in two attempts, and the number of team members who climbed the rock in two attempts is 20. b. Number of team members who climbed the rock = (Total team members Number of team members who did not attempt to climb) = 50 5 = 45 c. The number of team members who climbed the rock in not more than two attempts is 30. The team members who climbed the rock in one or two attempts come under this category Q3) If the juice contained in a cylindrical glass is poured into a hemispherical cup, then a. What is the percentage of juice that fills the cup? b. What is the percentage of juice that remains in the cylindrical glass? Answer Diameter of the hemispherical cup = 7 cm Diameter of tthe cylindrical glass = 7 cm Height of the cylindrical glass = 10.5 cm Volume of juice in the hemispherical cup =23r3=23727272cm3 = 89.83 cm3 Volume of the cylindrical glass =r2h=727210.5 cm3=404.25 cm3 Volume of juice in the cylindrical glass = 23 404.25 = 269.50 cm3 Volume of juice in the hemispherical cup = 89.75 cm3 a. Percentage of juice that fills the cup =Volume of the juice. In the hemispherical cupVolume of juice in cylindrical glass100=89.75269.50100=33.30 % b. Volume of the remaining juice = Volume of juice in the cylindrical glass Volume of juice in the hemispherical cup = 269.50 89.75 = 179.75 cm3

  • Q1) Consider the following information about the survey conducted by Sarah on the success rate of the team members of Brigadier Tripathi Team climbing the rock.

    No. of attempts No. of people

    1st attempt 10

    2nd attempt 20

    More than two attempts 15

    Did not attempt at all 5

    Total 50

    What is the mode of the number of times the team members tried climbing the rock? Answer Mode is the most frequently occurring observation. Here, the mode of the number of attempts is 2 Q2) If the juice contained in a hemispherical cup that is fully filled with juice is poured into a cylindrical glass, then: a. What percentage of the glass is filled with the juice? b. What percentage of the glass is empty? Answer Diameter of the hemispherical cup = 7 cm Diameter of the cylindrical glass = 7 cm Height of the cylindrical glass = 10.5 cm Volume of juice in the hemispherical cup =23r3=23727272 cm3=89.75 cm3 Volume of the cylindrical glass=r2h=727210.5 cm3=404.25 cm3 Volume of the cylindrical glass filled with juice = Volume of juice in the hemispherical

  • cup = 89.75 cm3 a. Percentage of the glass filled with juice Volume of cylindrical glass filled with juiceTotal Volume of the cylindrical glass100=89.75404.25100=22.20 % b. Volume of the empty cylindrical glass = Total volume of the cylindrical glass - Volume of cylindrical glass filled with juice = 404.25 89.75 = 314.5 cm3 Percentage of the glass that is empty =Empty Volume of cylindrical glassTotal Volume of the cylindrical glass100=314.5404.25100=77.8 %

    Q3) Two canvasses of area 551 m2 were given to the students to make a big tent in the shape of a cone above a cylinder. The stitching and wasting incurred while cutting amounted to 1 m2 each in both the canvasses. If the radii of canvasses are 7 m each, then what is the volume of air inside the tent? Answer For the tent made by joining cylindrical and conical tents: Volume of air inside the tent = Volume of the cylindrical tent + Volume of the conical tent =r2h+13r2h' For the cylindrical tent, we need to find the height of the tent. The area of the sheet should be 551 m2. 1 m2 is wasted in stitching, so Surface area of the cylindrical tent = 551 - 1 m2 = rh Or, 550 = 2 7 h Or, 55072227=h h = 12.5 m Volume of the cylindrical tent = r2h

  • = 7 7 12.5 = 1925 m3 Similarly, for the conical tent: Effective area of cone = 551 - 1 m2 = 550 m2 Area of cone = rl r = 7 m rl = 7 l = 550 l = 25 m Let h be the height of the cone. l2 = h'2 + r2 h'2 = l2 - r2 Or, h'2 = 576 Or, h' = 24 m Volume of the conical tent = 13 r2h' = 13 7 7 24= 1232 m3 3157 m3 Total volume of the tent = 1925 m3 + 1232 m3 = 3157 m3

    Q1) Out of the five team members of Brigadier Tripathi Team who did not attempt to climb the rock, one was selected to assist the teachers in preparing the performance chart of all the students. Use the given table to answer the question.

    Gender of team members

    Number of team members

    Male 2

    Female 3 What is the probability that the selected member is female? Answer Probability = total number of attempts in which event happenedTotal number of trials

  • Total number of team members who did not attempt to climb the rock = 5 Number of female members = 3 P (selected member is a female) =35

    Q2) After the survey conducted by Sarah on the success rate of the team members of Brigadier Tripathi Team who climbed the rock, she assigned groups to them.

    No. of attempts No. of people Group assigned

    1st attempt 10 A

    2nd attempt 20 B

    More than two attempts 15 C

    Did not attempt at all 5 D

    Total 50 Brigadier wanted to select one team member to guide the members of Sarah's team. Find the probability of selecting the team member from each group? What is the sum of all the probabilities found? Answer Solution: Probability=total number of attempts in which event happenedtotal number of trials a. Number of team members belonging to group A = 10 Total number of team members = 50 P(selecting the student from group A) =1050=0.2 b. Number of team members belonging to group B = 20 Total number of team members = 50 P(selecting the team members from group B) =2050=0.4

    Q3)

  • What is the ratio of the volumes of air inside the hemispherical- and conical-shaped tents with the same base area? Answer If the base area of the conical and hemispherical tent is the same, they must have the same radius, i.e., 7 m. To find the volume of the cone, we first need to find out the height of the cone. The conical tent uses one canvas of area 551 m2, in which 1 m2 is wasted in cutting and stitching. Effective area of cone = 551 - 1 m2 = 550 m2 Area of cone = rl r = 7 m rl = 7 l = 550 l = 25 m Let h be the height of the cone. l2 = h2 + r2 h2 = l2 - r2 Or, h2 = 576 Or, h = 24 m Volume of the conical tent 13r2h = 13 7 7 24 = 1232 m3 For the hemispherical tent: Radius = 7 m Volume of the hemispherical tent =23r3=23777=718.66 m3 Ratio of the volumes=volume of the conical tentvolume of the hemispherical tent=1232718.66=1.7:1

    Q1) To accommodate four students, one of the students made a tent in the shape of a prism having

  • a rectangular base of length 11 m, in which the same area is given to each student for resting as it is given in the conical tent. What is the breadth of the base of the tent? Answer As the area given to each student is the same as in the conical tent, the area of the base of the new tent is equal to the area of the base of the conical tent. Area of the base of the conical tent =7272 m2=772 m2 Area of the base of the new tent = Length Breadth = 11 Breadth =772 m2 Breadth =72=3.5m

    Q2) 1 m2 convas is wasted in cutting and stitching while making a tent. The tent can accomodate either four students or two teachers. What is the cost of the canvas that is wasted in the process if the cost of canvas is Rs 100 per m2? Answer Each tent can have four students. Total number of tents for students =604=15 Numbers of tents required to accommodate teachers =102=5 Total number of tents = 15 + 5 = 20 tents Canvas wasted in cutting and stitching a tent = 1 m2 Total canvas wasted = 20 1 = 20 m2 Cost of canvas that is wasted = 20 100 = Rs 2000

    Q3) The survey conducted by Sarah on the success rate of the team members of Brigadier Tripathi Team climbing the rock is represented in the form of a table given below.

    No. of attempts No. of people

    1st attempt 10

    1nd attempts 20

  • More than two attempts 15

    Did not attempt at all 5

    Total 50 Represent the given data in the form of a pie chart. Answer For 1st attempt:Number of team members who climbed the rock in 1st attemptTotal number of team members=1050360=72 For 2nd attempt:Number of team members who climbed the rock in 2nd attemptTotal number of team members=2050360=144 For more than two attempts: Number of team members who climbed the rock in morethan 2 attemptTotal number of team members=1550360=108 For did not attempt:Number of team members who did not attemptTotal number of team members=1550360=36

  • Q1) If a tent made from canvas is hemispherical in shape, then what is the radius of the tent? Answer Area of the canvas used = 551 m2 Effective area of the tent = 551 1 = 550 m2 Area of the hemisphere = 2r2 = 550 r2=5507222=2572 Or, r=572m=9.3541 m

    Q2) If one of the students makes a hemispherical tent with radius of base same as that of a conical tent so that each student gets the same area for resting as it is given in the conical tent, then what is the are