Question

The formula for the volume of a cone is V=13πr2h,V=\frac{1}{3}\pi r^2 h,V=31​πr2h, where r is the radius of the cone and h is the height of the cone. Rewrite the formula to solve for the positive value of rin terms of h and V.

Answer 1

r = √3V/√πh

Explanation:

V = 1/3πr²h

where,

V = volume of the cone

r = radius of the cone and

h = height of the cone.

Rewrite the formula to solve for the positive value of r in terms of h and V.

V = 1/3πr²h

V = 1/3 * π * r² * h

r² = V ÷ 1/3 * π * h

r² = V ÷ πh/3

r² = V × 3/πh

r² = 3V / πh

find the square root of both sides

√r² = √3V / πh

r = √3V/πh

Also written as

r = √3V/√πh