A bucket in the shape of a frustum has an upper diameter of 10 cm and a lower diameter of 4 cm. The frustum has a height of 3 cm.
The formula for the volume of a frustum is...
V = [h(B2 - B1)] / 3 where h represents the height, B2 is the area of the larger base, and B1 is the area of the smaller base.
First, lets find the area of the two bases.
Larger base (B2): A = pi * r^2 = pi * 5^2 = pi * 25 = 25`pi`
Smaller base (B1): A = pi * r^2 = pi * 2^2 = pi * 4 = 4`pi`
Remember, you must use radius instead of diameter. Thats why 10 changed to 5 and 4 changed to 2.
Now we use this in our volume formula.
[3(25`pi` - 4`pi` )] / 3
(3 * 21`pi` ) / 3 (the 3s will cancel)
The volume of the frustum is 21`pi` cubic cm