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Select the correct answer.
The figure shows a vertical cross section of a sphere inscribed in a right cone.

A vertical cross section of a sphere inside a cone has a radius labeled lowercase r. The height of the cone is 12 centimeters. The half-length of the face of the cone is 5 centimeters.

Find the volume of the sphere in terms of π.

Select the correct answer The figure shows a vertical cross section of a sphere inscribed in a right cone A vertical cross section of a sphere inside a cone has class=

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The volume of the sphere will be 49π cubic cm. Then the correct option is C.

What is the volume of the sphere?

Let r be the radius of the sphere.

Then the volume of the sphere will be

V = 4/3 πr³ cubic units

The figure shows a vertical cross-section of a sphere inscribed in a right cone.

A vertical cross-section of a sphere inside a cone has a radius labeled as r. The height of the cone is 12 centimeters. The half length of the face of the cone is 5 centimeters.

Then the volume of the sphere will be

In ΔADF, we have

tan a = 5 / 12

      a = 22.61°

Then in triangle ΔABC, we have

   sin 22.61° = r / (12 - r)

           0.38 = r / (12 - r)

4.62 - 0.38r = r

           1.38r = 4.62

                  r = 3.34 cm

Then the volume of the sphere will be

V = 4/3 π(3.34)³

V = 49π cubic cm

Then the correct option is C.

More about the volume of the sphere link is given below.

https://brainly.com/question/9994313

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