Need help on a calculation for a gravel pit

Question

I have a gravel pit $70$ inches in diameter on the inside. I want to make the pit $4$ inches deep in gravel. The bags come in $0.5$ cubic feet.

I can't even figure out how many cubic feet. How many bags would I need to do this? Any help would be greatly appreciated!

Answer 1

1. Get the volume of the pit: I guess the gravel pit is supposed to be in cylindric shape. The volume of a cylinder is (as in most geometric 3D-objects) given by

$$\text{volume}_{\text{cyl}}=(\text{area of base}) \cdot \text{height}.$$

The base is a circle which has area $r^2\pi$ where $r$ is the radius (which is half the diameter). Your height is 4 inches. Plug this in and you have the volume of the gravel pit in cubic inches you have to fill.

Computing that yields

$\text{volume}_{\text{cyl}}=(35 ~\mathrm{in})^2\pi\cdot 4~\mathrm{in}\approx 15393.80~\mathrm{in}^3.$

2. Get the volume of 1 bag: This is already given in the question. But you need to have the same units, so you might want to switch from $0.5$ cubic feet to $$\text{volume}_{\text{bag}}=864 ~\mathrm{in}^3.$$

3. Get the amount of bags: This is easily done by

$$\text{amount of bags} = \frac{\text{volume}_{\text{cyl}}}{\text{volume}_{\text{bag}}}.$$

Computing that yields

$\text{amount of bags} = \frac{15393.80~\mathrm{in}^3}{864 ~\mathrm{in}^3}\approx 17.82$

4. The aftermath: If the number you get from 3. is not an integer, you need to round that number up to the next integer since you can't buy fractions of bags. This means you'll need

$\lceil 17.82 \rceil=18$

bags.

Answer 2

For ease u can do conversions from inches to feet and proceed by formula of volume is π rsquare h. And then calculate a 0.5 cubic feet bag takes