Chapter 12.3, Problem 12PSC

To determine

To calculate: The total surface area of solid which contains cylinder of height 10.

Answer to Problem 12PSC

The total surface area of solid is $579.94$ .

Explanation of Solution

Given information:

Diameter of cylinder d = 6,

Height of cylinder = 10,

Height of prism = 8.

Formula used:

Area of cylinder $=C\times h$

C = Circumference of cylinder and h = height of cylinder

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle Area of a circle: $A=\pi r^2$

r = radius of circle

Calculation:

  

Lateral area of prism $=4\times b\times h$

Lateral area of prism $=4\times 10\times 8$

Lateral area of prism $=320$

Lateral Area of cylinder $=C\times h$

Lateral Area of cylinder $=6\pi \times 10$

Lateral Area of cylinder $=60\pi$

a = base of prism = 8

h = height of prism = 8

Area of prism base $=a\times h$

Area of prism base $=8\times 8$

Area of prism base $=64$

Area of cylindrical base $=\pi r^2$

Area of cylindrical base $=\pi {\left(3\right)}^2$

Area of cylindrical base $=9\pi$

Total Area = Lateral area of prism + Lateral Area of cylinder + 2 (Area of prism base -

Area of cylindrical base)

Total Area $=320+60\pi +2(64-9\pi )$

Total Area $=320+60\pi +128-18\pi$

Total Area $=448+42\pi$

Total Area $=579.94$