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In Mathematics / High School | 2025-07-03

A swimming pool is being filled with water. The diameter of the pool is 27 feet, and the height is 4 feet. Which formula best represents the volume of the pool?

[tex]V=(113.5)(4)[/tex]
[tex]V=(135)^2(4)[/tex]
[tex]V=(-27)(4)[/tex]
[tex]V=(-27)^2(4)[/tex]

Asked by caydencole0414

Answer (2)

Recognize the swimming pool as a cylinder and recall the volume formula: V = π r 2 h .
Calculate the radius from the given diameter: r = 2 27 ​ = 13.5 feet.
Substitute the radius and height into the volume formula: V = π ( 13.5 ) 2 ( 4 ) .
The formula that best represents the volume of the pool is: V = ( 13.5 ) 2 ( 4 ) ​

Explanation

Problem Analysis The problem asks us to identify the formula that represents the volume of a cylindrical swimming pool, given its diameter and height. We need to recall the formula for the volume of a cylinder and apply the given dimensions to find the correct expression.

Volume of a Cylinder The swimming pool is in the shape of a cylinder. The formula for the volume V of a cylinder is given by: V = π r 2 h where r is the radius of the base and h is the height of the cylinder.

Calculate the Radius We are given that the diameter of the pool is 27 feet. The radius r is half of the diameter, so we calculate the radius: r = 2 d ​ = 2 27 ​ = 13.5 feet The height of the pool is given as h = 4 feet.

Substitute Values into the Formula Now, we substitute the values of the radius r = 13.5 feet and the height h = 4 feet into the volume formula: V = π ( 13.5 ) 2 ( 4 ) This formula represents the volume of the swimming pool.

Identify the Correct Formula Comparing the derived formula V = π ( 13.5 ) 2 ( 4 ) with the given options, we see that the closest representation is: V = ( 13.5 ) 2 ( 4 )


Examples
Understanding the volume of a cylinder is useful in many real-life situations. For example, when designing cylindrical storage tanks for liquids or gases, engineers need to calculate the volume accurately to ensure the tanks can hold the required amount. Similarly, in architecture, calculating the volume of cylindrical columns is essential for determining the amount of material needed and the structural integrity of the building. Even in cooking, understanding the volume of cylindrical containers helps in measuring ingredients accurately.

Answered by GinnyAnswer | 2025-07-03

The volume of a cylindrical swimming pool can be calculated using the formula V = π r 2 h . For a pool with a diameter of 27 feet and a height of 4 feet, the radius is 13.5 feet, leading to the formula V = ( 13.5 ) 2 ( 4 ) . Therefore, the correct choice is: V = ( 13.5 ) 2 ( 4 ) ​
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Answered by Anonymous | 2025-07-04

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