Capacity and cubic feet point to volume, the space inside a solid, rather than surface area. For a cylinder, multiply the circular base area by the height to find its full capacity. Then take the stated percent of that capacity, using Desmos for the arithmetic. The percent is not a height in feet, and full capacity is not yet the amount of water.
Hints
- Hint 1
A cylinder has a circular base with area . To find the space inside, multiply that area by the height. Which given length belongs in , and which belongs in ?
- Hint 2
The cylinder's volume gives its full capacity. A percent names a fraction of a whole, so a tank that is full holds of that capacity. What volume should you take of?
Step-by-step
Find full capacity, then take 80%
Step 1Write the cylinder's full-volume expression
A cylinder's circular base has area ; multiplying by its height gives its volume, or space inside. The given radius, the center-to-edge distance, is feet. With height feet and the given , the full capacity is .
- Step 2
Calculate the full capacity
Type in Desmos. It shows , the tank's full capacity in cubic feet. That isn't the water volume yet.
- Step 3
Identify what the percent applies to
Let be the water's volume. Since the tank is 80% full, and percent means “out of 100,” write . Take the percent of the full volume, not as a number of feet of height.
- Step 4
Find the water volume
Type in Desmos. It prints , so the volume of water is cubic feet. Choice C.