Question

A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown. Which expression represents the volume, in cubic units, of the frustum? π(7.52)(11) – π(3.52)(8) π(7.52)(11) + π(3.52)(8) π(7.52)(19) – π(3.52)(8) π(7.52)(19) + π(3.52)(8)

Answer 1

Volume of Frustum having , H= 11 units, Larger radius (R)= 7.5 units , and Smaller radius(r) =3.5 units is given by=

 $\frac{\pi\times H}{3} \times (R^2+R r+r^2)$

Or, the volume of frustum can be calculated  by

= Volume of larger cone - volume of smaller cone

$=\frac{\pi }{3}\times [(7.5)^2\times 19]-\frac{\pi }{3}\times [(3.5)^2\times 8]$

As, total height= 11 +8=19 units, radius of smaller cone= 3.5 units

Radius of whole cone = 7.5 units

Option (C)

Answer 2

Think of the two pieces together as a single cone of height 19, and its volume.
Then think of only the upper piece as a cone, and find its volume.
The volume of the frustum is the total volume minus the volume of the upper piece.

The volume of a cone is:

$V = \dfrac{1}{3} \pi r^2 h$

Total volume:

$V_t = \dfrac{1}{3} \times \pi \times 7.5^2 \times 19$

Volume of upper cone:

$V_u = \dfrac{1}{3} \times \pi \times 3.5^2 \times 8$

Volume of frustum:

$V_f = \dfrac{1}{3}\pi(7.5^2)(19) - \dfrac{1}{3}\pi(3.5^2)(8)$