The truncated right circular cone below has a large base radius $8$ cm and a small base radius of $4$ cm. The height of the truncated cone is $10$ cm. The volume of this solid is $n \pi$ cubic cm, where $n$ is an integer. What is $n$?
+128731 This solid is known as a frustum.....
Volume of frustum, V = H3(S1+S2+√S1S2), where
H = Height of the frustum (the distance between the centers of two bases of the frustum)
S1 = Area of one base of the frustum
S2 = Area of the other base of the frustum
Area of large base = pi *(8)^2 = 64 pi
Area of small base = pi* (4)^2 = 16pi
Volume = (1/3) (10cm) ( 64 pi + 16 pi + sqrt ( 64 pi * 4 pi) ) =
(10/3) (64 pi + 16pi + sqrt (256 pi^2) ) =
(10/3) ( 64 pi + 16 pi + 16 pi) =
10 ( 96 pi) / 3 =
320 pi cm^2
n = 320
