Question

A cylinder, cone, and sphere are shown below. The three figures have the same radius.

If the radius is 3, what is each volume?

Answer 1

The volume of a cylinder with radius r and height h is given by:

V = πr^2h

The volume of a cone with radius r and height h is given by:

V = (1/3)πr^2h

The volume of a sphere with radius r is given by:

V = (4/3)πr^3

If the radius is 3, then we can calculate the volumes of the three figures as follows:

Cylinder:

V = πr^2h = π(3)^2(6) = 54π

Cone:

V = (1/3)πr^2h = (1/3)π(3)^2(4) = 12π

Sphere:

V = (4/3)πr^3 = (4/3)π(3)^3 = 36π

Therefore, the volume of the cylinder is 54π, the volume of the cone is 12π, and the volume of the sphere is 36π.

Answer 2

Answer: it is below with each of the formulas to solve each shape

Explanation:

Cylinder volume formula: V ≈ πr²h

Cone volume formula: V = 1/3πr²h

Sphere volume formula: V = 4/3πr³

The cylinder has a volume of around 84, but since there is no option, no shape has this volume

The cone has a volume of 27π

The sphere has a volume of 36π

I hope this helps you