Chapter 12.5, Problem 29PPS

a.

To determine

To determine the volume of the planter.

Answer to Problem 29PPS

614.53 cubic inches

Explanation of Solution

Given:

  

  $R=5.5$ inches, $r=3.25$ inches and $h=10$ inches

Formula used:

Volume of a frustum $=\frac{1}{3}\pi h(R^2+r^2+R\ast r)$

where $R$ is the bigger radius , $r$ is the smaller radius and $h$ is the height of the frustum.

Calculation:

The planter represents the shape of a frustum.

So volume of the planter $=\frac{1}{3}\pi h(R^2+r^2+R\ast r)$

Now putting the values,

  $\Rightarrow \frac{1}{3}3.14\times 10({5.5}^2+{3.25}^2+5.5\ast 3.25)$

On solving,

  $\Rightarrow 614.23$ cubic inches

This situation is helpful because it will help the person to buy the amount of soil for the planter.

Conclusion:

Therefore, the volume of the planter is 614.23 cubic inches.

b.

To determine

To find the number of planters could be filled with one bag of potting soil.

Answer to Problem 29PPS

0.11

Explanation of Solution

Given:

A planter with volume 614.23 cubic inches.

Volume of 1 potting soil bag is 3 cubic foot.

Formula used:

1 cubic foot $=$ 1728 cubic inches

Calculation:

Volume of 1 bag of potting soil $=3$ cubic foot

  $\Rightarrow 1728\times 3$ cubic inches

Now number of planters could be filled with one bag of potting soil $=$ volume of planter divided by volume of 1 bag.

  $\Rightarrow \frac{614.23}{1728\times 3}$

  $\Rightarrow 0.11$

Conclusion:

Therefore, 0.11 planters could be filled with one bag of potting soil.