Question

The large sphere has a diameter of 20 feet. Which expression represents the volume, in cubic units, of the shaded part of the sphere?

a) 2(109) + 37(4)
b) 10(10) - 1(49)
c) 7(20) + 7(4)
d) 7(20) - 1(43)

Answer 1

The volume of the shaded part of the sphere can be calculated by subtracting the volume of the smaller sphere from the volume of the larger sphere. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. In this case, the volume of the shaded part of the sphere is 3500π cubic units.

Step-by-step explanation:

The volume of a shaded part of the sphere can be calculated by subtracting the volume of the smaller sphere from the volume of the larger sphere.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

In this case, the diameter of the larger sphere is 20 feet, so the radius is 10 feet.

The volume of the larger sphere is V1 = (4/3)π(10)³ = (4/3)π1000 = 4000π cubic units.

The volume of the smaller sphere can be calculated using the same formula, but with a radius of 5 feet (half of the diameter of the larger sphere).

The volume of the smaller sphere is V2 = (4/3)π(5)³ = (4/3)π125 = 500π cubic units.

Therefore, the volume of the shaded part of the sphere is V1 - V2 = 4000π - 500π = 3500π cubic units.