Question

Begin with a sphere of radius r and bore a hole into the sphere in the shape of a right circular cylinder, leaving only a band of height h. Find the volume of the resulting shape.

a) Volume = X
b) Volume = Y
c) Volume = Z
d) Volume = W

Answer 1

To find the volume of the resulting shape, calculate the volume of the cylinder and subtract it from the volume of the original sphere.

Step-by-step explanation:

To find the volume of the resulting shape, we first need to calculate the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h. Plugging in the given values, we get:

V = 3.142 × (0.750 cm)² × 5.25 cm = 9.278 cm³

Next, we need to subtract the volume of the cylinder from the volume of the original sphere. The formula for the volume of a sphere is V = 4/3πr³. Since we are only left with a band of height h, the remaining volume of the sphere would be:

V = 4/3πr³ - 9.278 cm³

This is the volume of the resulting shape.