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

V = π(7.5)²(19) - π(3.5)²(8)

Explanation:

Think of the upper cone being attached to the frustum forming a larger, taller cone. Find the volume of the larger cone. Then find the volume of the smaller, upper cone. The volume of the frustum is the difference of the two volumes.

V = πR²H - πr²h

V = π(7.5)²(19) - π(3.5)²(8)

Answer 2

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

`(\pi* H)/(3) * (R^2+R r+r^2)`

Or, the volume of frustum can be calculated by

= Volume of larger cone - volume of smaller cone

`=(\pi )/(3)* [(7.5)^2* 19]-(\pi )/(3)* [(3.5)^2* 8]`

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

Radius of whole cone = 7.5 units

Option (C)