Question

The radius of a cylinder is twice as long as the radius of a​ cone, and the height of the cylinder is half as long as the height of the cone. What is the ratio of the volume of the cylinder to that of the​ cone?

Answer 1

The ratio of the volume of a cylinder to that of a cone as described in the question is; 6 : 1.

According to the question;

• r(cylinder) = 2r(cone)

• h(cylinder) = h(cone)/2

• The volume of a cylinder is given by;

• V(cylinder) = π r² h

• V(cone) = (π r² h)/3

By substituting values;

• π × (2r(cone))²× h(cone)/2 = π × (r(cone))² × h(cone)/3

By cancellation of common terms in each side of the equation; we are left with;

2 = 1/3

By dividing through by 1/3; the ratio of the volume of the cylinder to that of the cone is;

6 : 1.

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