Question

The volume of a cone varies jointly with the base (area) and the height. The volume is 12.5 ft3 when the base (area) is 15 ft2 and the height is 212 ft. Find the volume of the cone (after finding the variation constant) when the base (area) is 12 ft2 and the height is 6 ft

Answer 1

Answer:

the volume of the cone is V=0.283ft³

Step-by-step explanation:

From the question, we know that we are dealing with variation.

Then the variation can be interpreted as

V=kAh

Where K= constant of proportionality

Volume V= 12.5ft³

Height of cone h=212 ft.

Area of base of cone A= 15ft²

Then if we substitute into the expresion above, we have

12 .5= K × 15×212

K= 12.5/(15×212)

K=0.00393

Then when the base (area) is 12 ft² and the height is 6 ft

V=V=kAh

Substitute the new values we have

V= 0.00393× 12×6

V=0.283ft

Therefore, the volume of the cone is V=0.283ft³