Question

The volume of a cone varies jointly as the height of the cone and the area of the base. The volume of a cone with height 30 centimeters and base 14 centimeters squared is 140 centimeters cubed. Find the volume of a cone with height 7 centimeters and base 12 centimeters squared.

Answer 1

Explanation:

Below is an attachment containing the solution.

Answer 2

V₂=28cm³

Explanation:

Way 1

The volume of a cone is
`V=(\pi r^(2)h)/(3)`, and h₁ = 30 cm but the base (Ba₁) is 14 cm², so

`V=(Ba.h)/(3)`, where Ba= Base area

if h₂=7cm and Ba₂=12cm² then

`V_(1) =(12cm^(2).7cm)/(3)=28cm^(3)`

Way2

If the volume of a cone varies jointly as the height of the cone and the area of the base, then we must find the relationship between the bases and heights of the cones

Ba₁*h₁ = 30cm*14cm² = 420cm³

Ba²*h²= 7cm*12cm² = 84cm³

420/84 = 5; ratio = 5 also

V₂=V₁/5 ⇒ V₂=140cm³/5 = 28cm³