Question

The right circular cone has radius 2p and height 5p. the volume of the cone is 22500pi. work out the value of p?

A) 3
B) 5
C) 6
D) 8

Answer 1

To find the value of p, we can use the formula for the volume of a cone and solve for p using the given values of the radius, height, and volume.

Step-by-step explanation:

To find the value of p, we can use the formula for the volume of a cone: V = 1/3 × π × r² × h. In this case, the volume of the cone is given as 22500π. We are also given that the radius is 2p and the height is 5p. Substituting these values into the formula, we get:

22500π = 1/3 × π × (2p)² × 5p

Simplifying, we have:

22500 = 1/3 × 4 × p² × p × 5

This can be further simplified to:

22500 = 4/3 × 5 × p³

Multiplying both sides by 3/20, we get:

p³ = 337.5

Taking the cube root of both sides, we find that p = 6. Therefore, the value of p is 6.