Chapter 12, Problem 19RP

To determine

To calculate: The total area of cylinder part.

Answer to Problem 19RP

The total area of cylinder part is $270.79$ .

Explanation of Solution

Given information:

Radius of cylinder r = 6,

Height of cylinder h = 10.

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:

  

Area of cylinder $=C\times h$

The part is $\frac{1}{4}$ of cylinder.

  $\begin{array}{l}C=2\pi r\\ C=2\pi \times 6\\ C=12\pi \\ h=10\end{array}$

Area of cylinder $=\frac{1}{4}\times C\times h$

Area of cylinder $=\frac{1}{4}\times 12\pi \times 10$

Area of cylinder $=3\pi \times 10$

Area of cylinder $=30\pi$

There are two rectangles perpendicular to each other.

Area of rectangle $=2\left(10\times 6\right)$

Area of rectangle $=120$

Two half of semicircles are used.

Area of half semicircle $=2\times \frac{1}{4}\pi {\left(6\right)}^2$

Area of half semicircle $=\frac{1}{2}\times 36\pi$

Area of half semicircle $=18\pi$

Total area of cylinder = Area of cylinder + Area of rectangle + Area of half semicircle Total area of cylinder $=30\pi +120+18\pi$

Total area of cylinder $=48\pi +120$

Total area of cylinder $=270.79$