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What is the volume of a right circular cylinder with its base's diameter of 11.6 and height of 19.2? Use л = 3.14 as needed. Round to two decimal places as needed.

What is the volume of a right circular cylinder with its base's diameter of 11.6 and height of 19.2? Use л = 3.14 as needed. Round to two decimal places as needed.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Problem Statement **What is the volume of a right circular cylinder with its base's diameter of 11.6 and height of 19.2?** Use \(\pi = 3.14\) as needed. Round to two decimal places as needed. #### Explanation: To solve this problem, we'll use the formula for the volume of a right circular cylinder: \[ V = \pi r^2 h \] Where: - \( V \) is the volume - \( \pi \) (pi) is a constant approximately equal to 3.14 - \( r \) is the radius of the base of the cylinder - \( h \) is the height of the cylinder First, we need to find the radius of the base. Since the diameter is given \(d = 11.6\), the radius \(r\) is half of the diameter: \[ r = \frac{d}{2} = \frac{11.6}{2} = 5.8 \] Next, we plug the values into the volume formula: \[ V = 3.14 \times (5.8)^2 \times 19.2 \] Calculating the radius squared: \[ r^2 = 5.8^2 = 33.64 \] Now, substitute all known values into the volume formula: \[ V = 3.14 \times 33.64 \times 19.2 \] \[ V = 2116.30 \] Thus, the volume of the right circular cylinder is approximately \(2116.30\) cubic units, rounded to two decimal places.
Transcribed Image Text:### Problem Statement **What is the volume of a right circular cylinder with its base's diameter of 11.6 and height of 19.2?** Use \(\pi = 3.14\) as needed. Round to two decimal places as needed. #### Explanation: To solve this problem, we'll use the formula for the volume of a right circular cylinder: \[ V = \pi r^2 h \] Where: - \( V \) is the volume - \( \pi \) (pi) is a constant approximately equal to 3.14 - \( r \) is the radius of the base of the cylinder - \( h \) is the height of the cylinder First, we need to find the radius of the base. Since the diameter is given \(d = 11.6\), the radius \(r\) is half of the diameter: \[ r = \frac{d}{2} = \frac{11.6}{2} = 5.8 \] Next, we plug the values into the volume formula: \[ V = 3.14 \times (5.8)^2 \times 19.2 \] Calculating the radius squared: \[ r^2 = 5.8^2 = 33.64 \] Now, substitute all known values into the volume formula: \[ V = 3.14 \times 33.64 \times 19.2 \] \[ V = 2116.30 \] Thus, the volume of the right circular cylinder is approximately \(2116.30\) cubic units, rounded to two decimal places.
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