If the exact volume of rignt circular Cylinder is 200 r cm3 and it's altidude measures 8cm, what is the measure Of the radius of the circular base?
If the exact volume of rignt circular Cylinder is 200 r cm3 and it's altidude measures 8cm, what is the measure Of the radius of the circular base?
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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Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
![**Volume Calculation of a Right Circular Cylinder**
*Exercise 9:*
If the exact volume of a right circular cylinder is \(200\pi \, \text{cm}^3 \) and its altitude measures 8 cm, what is the measure of the radius of the circular base?
---
To solve this, we can use the formula for the volume of a right circular cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height (altitude)
Given:
- \( V = 200\pi \, \text{cm}^3 \)
- \( h = 8 \, \text{cm} \)
We need to find the radius \( r \).
Let's substitute the known values into the volume formula and solve for \( r \):
\[ 200\pi = \pi r^2 \cdot 8 \]
Simplify by dividing both sides by \( \pi \):
\[ 200 = r^2 \cdot 8 \]
Then divide both sides by 8:
\[ 25 = r^2 \]
Finally, take the square root of both sides:
\[ r = \sqrt{25} \]
\[ r = 5 \, \text{cm} \]
Thus, the radius of the circular base is 5 cm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55a87db1-34dd-4361-bb49-0fd4dde658a5%2F584c606d-5a0a-4061-b84c-41abccb1c5f9%2Fzjhlz4.jpeg&w=3840&q=75)
Transcribed Image Text:**Volume Calculation of a Right Circular Cylinder**
*Exercise 9:*
If the exact volume of a right circular cylinder is \(200\pi \, \text{cm}^3 \) and its altitude measures 8 cm, what is the measure of the radius of the circular base?
---
To solve this, we can use the formula for the volume of a right circular cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height (altitude)
Given:
- \( V = 200\pi \, \text{cm}^3 \)
- \( h = 8 \, \text{cm} \)
We need to find the radius \( r \).
Let's substitute the known values into the volume formula and solve for \( r \):
\[ 200\pi = \pi r^2 \cdot 8 \]
Simplify by dividing both sides by \( \pi \):
\[ 200 = r^2 \cdot 8 \]
Then divide both sides by 8:
\[ 25 = r^2 \]
Finally, take the square root of both sides:
\[ r = \sqrt{25} \]
\[ r = 5 \, \text{cm} \]
Thus, the radius of the circular base is 5 cm.
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