Mathcad - Volumes and Plane Areas.xmcd

Provide the area formulas and values for the given solids

1. Hexagon (A pentagon of 6 sides)

S 6

A 1.5 S 3.67

2. Trapezoid

a 7 b 4 h 5

Aa b

2

h 27.5

3. Rhombus

d1 10 d2 8 Ad1 d2

240.0

4. Circle

R 8

A π R2

201

Julio C. Banks, PE page 1 of 4

Mathcad - Volumes and Plane Areas.xmcd

5. Sector of a circleR 7

α 50°

ΔA απ rad

180°

R 6.11

Note: Mathcad performs unit conversion automatically, i.e., ΔA αR 6.11

6. Triangle

b 20 h 12

A1

2bh 120

7. Find (a) Slope, (b) Midpoint, and (c) Distance for (-12,6), (-5,-1). Show each formula and give the numerical results.

X 12 5( )T

Y 5 1( )T

Solution ΔY Y2 Y1 ΔX X2 X1 7.00

(a) SlopeΔY

ΔX0.5714

(b) XMPX1 X2

2

8.50 YMPY1 Y2

2

3.00

(c) Distance ΔX2

ΔY2 8.06

Julio C. Banks, PE page 2 of 4

Mathcad - Volumes and Plane Areas.xmcd

8. Find x, then, what are the three trigonometric function and their values for angle C

y 18 c 30

Solution

Pythagorean Theorem: x2

y2 c

2=

x c2

y2 24.0

Sinθy

c0.600 Cosθ

x

c0.800 Tanθ

y

x0.750

θ atany

x

36.9°

9-12 Provide the volume formulas and values for the given solids

9. Cube a 6 b 14 c 10

V abc 840

Julio C. Banks, PE page 3 of 4

Mathcad - Volumes and Plane Areas.xmcd

10. Sphere

R 9

V4

3π R

33054

11. Cylinder

R 5

h 12

V A h= where A π R2

78.5

Therefore, V A h 942 or V π R2h 942

11. 12. Right Cone

R 5

h 12

V1

3A h= where A π R

278.5

Therefore, V1

3A h 314 or V

1

3π R

2h 314

Julio C. Banks, PE page 4 of 4