Question

1. find the volume of the right circular cone given the diameter (d = 8 ft), (h=\frac{1}{3}d). find the volume of the sphere in terms of (pi) and to the nearest cubic foot.
2. a sphere has a radius of 10 feet. find the volume of the sphere in terms of (pi) and to the nearest cubic foot.
3. find the volume of the following figure:
4. the height of the pyramid is 4 inches, and the base is a rectangle 6 inches long and 3 1/2 inches wide. find the volume.
5. a square pyramid has a volume of (81ft^{3}). if the height of the pyramid is 9ft, find the area of the base.

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. Given $r = 10$ feet.
$V=\frac{4}{3}\pi(10)^{3}$

Step2: Calculate volume in terms of $\pi$

$V=\frac{4}{3}\pi\times1000=\frac{4000}{3}\pi$ cubic - feet.

Step3: Calculate numerical value

$V=\frac{4000}{3}\times3.14159\approx4188.79$ cubic - feet $\approx4189$ cubic - feet (to the nearest cubic foot)

Answer:

In terms of $\pi$: $\frac{4000}{3}\pi$ cubic feet; To the nearest cubic foot: $4189$ cubic feet