The volume of the sphere will be 49π cubic cm. Then the correct option is C.
<h3>What is the volume of the sphere?</h3>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.
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