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A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed within the cylinder, and then the cylinder is filled with water. How much water is in the cylinder? Give your answer in terms of pi. 576π in3 591π in3 540π in3 504π in3

Sagot :

Answer:

504 π in³

Step-by-step explanation:

Step 1

We find the volume of the cylinder

The formula for the volume of the cylinder = πr²h

A cylinder has a 12-inch diameter and is 15 inches tall.

Diameter = 12 inches, Radius = Diameter/2 = 12 inches/2 = 6 inches

Volume of the cylinder = π × 6² × 15

= 540π in³

Step 2

We find the volume of the ball.

A ball is spherical in shape

The formula for the Volume of a sphere = 4/3πr³

A 6-inch-diameter ball is placed within the cylinder.

The diameter of the ball = 6 inches

Radius = Diameter/2 = 6/2 = 3 inches

The volume of the ball =

4/3 × π × 3³

= 36π in³

Step 3

The amount of water in the cylinder is calculated as:

Volume of Cylinder - Volume of the ball

= 540 π in³ - 36 π in³

= 504 π in³

Answer:

504 π in³

Step-by-step explanation:

I got it right on the test :)

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