Chapter 12.4, Problem 20WE

To determine

To find: Approximately how many cans are needed to paint the rest of the silo’s exterior.

Answer to Problem 20WE

Cans needed to paint rest of the silo is 8.

Explanation of Solution

Given information:

From the given figure height of the silo is 20 m and diameter of the silo is 10 m.

Calculation:

The area of cylinder is given by

  $A=2\pi rh$ where $r$ is the radius of the cylinder and h is the height.

Also, area of the hemisphere is given by

  $A=2\pi r^2$ where $r$ is the radius of the hemisphere.

First find the area covered by one can,

  $\begin{array}{l}\text{Area covered by 2 can}=\text{Area of the hemisphere}\\ \text{Area covered by 2 can}=2\pi r^2\\ \text{Area covered by 2 can}=2\pi {\left(5\right)}^2\\ \text{Area covered by 2 can}=2\pi \times 25\\ \text{Area covered by 2 can}=50\pi {\text{ m}}^2\\ \text{Area covered by 1 can}=\frac{50}{2}\pi {\text{ m}}^2\\ \text{Area covered by 1 can}=25\pi {\text{ m}}^2\end{array}$

Now, calculate the can needed to paint the rest of the silo’s exterior.

  $\begin{array}{l}\text{Cans needed to paint rest of the silo exterior}=\frac{\text{Area of the cylinder}}{\text{Area covered 1 can}}\\ \text{Cans needed to paint rest of the silo exterior}=\frac{2\pi \left(5\right)\left(20\right)}{25\pi }\\ \text{Cans needed to paint rest of the silo exterior}=\frac{200\pi }{25\pi }\\ \text{Cans needed to paint rest of the silo exterior}=8\end{array}$

Hence,

Cans needed to paint rest of the silo is 8.