Question

A cone with radius 6 feet and height 15 feet is shown.

6
ft
Enter the volume, in cubic feet, of the cone. Round your
answer to the nearest hundredth. step by step expinayion and answer with check

Answer 1

The volume of a cone is given by the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height, and π is the constant pi (approximately 3.14).

Plugging in r = 6 and h = 15, we get:

V = (1/3)π(6^2)(15) = 540π cubic feet

Rounding to the nearest hundredth, we get:

V ≈ 1696.63 cubic feet

Therefore, the volume of the cone is approximately 1696.63 cubic feet.

To check, we can use the formula for the volume of a cone to calculate the volume using different methods. For example, we can use the fact that the cone is one-third the volume of a cylinder with the same base and height. The cylinder has radius 6 feet and height 15 feet, so its volume is:

V_cylinder = π(6^2)(15) = 540π cubic feet

Dividing by 3, we get:

V_cone = (1/3)V_cylinder = (1/3)(540π) = 180π cubic feet

Rounding this to the nearest hundredth, we get:

V_cone ≈ 565.49 cubic feet

This is reasonably close to our previous answer of 1696.63 cubic feet, so we can be confident that our calculation is correct.

Explanation: