Chapter 12.4, Problem 21WE

To determine

To find: How many cans will be needed to paint the ceiling.

Answer to Problem 21WE

Cans needed to paint the ceiling is 6.

Explanation of Solution

Given information:

An experimental one-room is a hemisphere with a floor and three cans of paint are needed to cover the floor.

Calculation:

Area of the hemisphere is given by

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

And, area of the circle is given by

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

First find the area covered by one can,

  $\begin{array}{l}\text{Area covered by 3 can}=\text{Area of the floor}\\ \text{Area covered by 3 can}=\pi r^2\\ \text{Area covered by 1 can}=\frac{\pi r^2}{3}\end{array}$

Now, calculate the can needed to paint the ceiling.

  $\begin{array}{l}\text{Cans needed to paint the ceiling}=\frac{\text{Area of the hemisphere}}{\text{Area covered 1 can}}\\ \text{Cans needed to paint the ceiling}=\frac{2\pi r^2}{\frac{\pi r^2}{3}}\\ \text{Cans needed to paint the ceiling}=6\end{array}$

Hence,

Cans needed to paint the ceiling is 6.