Question

Two solids are described in the list below.
One solid is a sphere and has a radius of 6 inches.
The other solid is a cylinder with a radius of 6 inches and a height of 6 inches.
what is the difference betwen the volumes in cubic inches of the solids in terms of pi

A.72pi
B.144pi
C.216pi
D.288pi​

Answer 1

The difference between the volumes in cubic inches is option A) 72pi

Step-by-step explanation:

• Volume of the sphere = 4/3 πr³
• radius r = 6 inches

Volume = 4/3 π(6)³

⇒ 4/3(216)π

⇒ 4$\times$72π

⇒ 288π cubic inches

• Volume of  a cylinder = π r²h
• radius r = 6 inches
• height h = 6 inches

Volume = π(6)²(6)

⇒ 6³π

⇒ 216π cubic inches

Difference between the volumes = 288π - 216π = 72π

Answer 2

The difference in volume between the two solids is 226.08in^3

Data;

• radius of sphere = 6in
• radius of cylinder = 6in
• height of cylinder = 6in

Volume of Sphere

The volume of a sphere is given as

$v = \frac{4}{3} \pi r^3$

Let's substitute the values and find the volume

$v = \frac{4}{3}*3.14*6^3\\v = 904.32in^3$

Volume of Cylinder

The formula of volume of a cylinder is given as

$v = \pi r^2 h$

Let's substitute the values into the equation and solve

$v = 3.14 * 6^2 * 6\\v = 678.24in^3$

The difference in volume between the two solids is

$volume of sphere - volume of cylinder = 904.32 - 678.24 = 226.08in^3$

The difference in volume between the two solids is 226.08in^3

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