A vessel is in the form of a frustum of a cone. Its radius at one end and the height are 8 cm and 14 cm respectively. If its volume is , then find the radius at the other end.

GIVEN :

Volume of the frustum cone “V” =

Radius of another end = “r”

Radius (R) = 8 cm

height (h) = 14 cm

we take π =

TO FIND : Radius of another end = ?

PRODEDURE :

As we know, the volume of frustum of cone,

×π ×h×(R² + r² + R×r) =

××(14)×(8² + r² + 8×r) =

(8² + r² + 8×r) = × 3 × ×

(64 + r² + 8r) = 258× 7×

(64 + r² + 8r) =

r² + 8r + 64 = 129

r² + 8r + 64 -129 = 0

r² + 8r - 65 = 0

(r + 13) (r - 5) = 0

r + 13 = 0 or r - 5 = 0

r = -13 or r = 5 cm

as the radius cannot be negative,

∴ the required radius = 5cm.