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
Related questions
Concept explainers
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
![**Question 5:** A cone has a surface area of \(200\pi\) square inches. If the radius of the cone is 10 inches, find the length of the slant height.
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The problem requires you to find the slant height of a cone provided its surface area and radius.
- **Given**:
- Surface area (\(A\)): \(200\pi\) square inches
- Radius (\(r\)): 10 inches
To solve for the slant height (\(l\)), use the formula for the surface area of a cone:
\[ A = \pi r (r + l) \]
By substituting the given values:
\[ 200\pi = \pi \times 10 \times (10 + l) \]
Simplify by dividing both sides by \(\pi\):
\[ 200 = 10 \times (10 + l) \]
Divide both sides by 10 to isolate \(l\):
\[ 20 = 10 + l \]
Subtract 10 from both sides:
\[ l = 10 \]
Thus, the length of the slant height is **10 inches**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3270e33a-773c-4d59-a44c-8e0b9afaafb6%2F0f69987f-2208-40a9-8a67-2123fb9087f8%2Fczrgwgn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5:** A cone has a surface area of \(200\pi\) square inches. If the radius of the cone is 10 inches, find the length of the slant height.
---
The problem requires you to find the slant height of a cone provided its surface area and radius.
- **Given**:
- Surface area (\(A\)): \(200\pi\) square inches
- Radius (\(r\)): 10 inches
To solve for the slant height (\(l\)), use the formula for the surface area of a cone:
\[ A = \pi r (r + l) \]
By substituting the given values:
\[ 200\pi = \pi \times 10 \times (10 + l) \]
Simplify by dividing both sides by \(\pi\):
\[ 200 = 10 \times (10 + l) \]
Divide both sides by 10 to isolate \(l\):
\[ 20 = 10 + l \]
Subtract 10 from both sides:
\[ l = 10 \]
Thus, the length of the slant height is **10 inches**.
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