A right cone has a surface area of 440 square inches and a radius of 7 inches. 13 Find the volume of the cone. Round to the nearest hundredth. 18 mi 18 mi Your answer URL allows OPEN BLANK FORM und to the nearest hundredth.
A right cone has a surface area of 440 square inches and a radius of 7 inches. 13 Find the volume of the cone. Round to the nearest hundredth. 18 mi 18 mi Your answer URL allows OPEN BLANK FORM und to the nearest hundredth.
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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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
Find the volume of the cone
![**Educational Content: Calculating Volume of a Cone**
### Problem Statement:
Find the volume of the cone. Round to the nearest hundredth.
#### Diagram Description:
There is a diagram of a right cone. The height of the cone is labeled as 18 miles (mi), and the radius of the base of the cone is also labeled as 18 miles (mi).
### Solution:
To find the volume \( V \) of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( \pi \) (pi) is approximately 3.14159.
- \( r \) is the radius of the base of the cone.
- \( h \) is the height of the cone.
Given:
- \( r = 18 \) mi
- \( h = 18 \) mi
Substitute the given values into the formula:
\[ V = \frac{1}{3} \pi (18)^2 (18) \]
First, calculate \( r^2 \) (the square of the radius):
\[ 18^2 = 324 \]
Next, multiply this result by the height of the cone:
\[ 324 \times 18 = 5832 \]
Now, multiply by \( \pi \):
\[ 5832 \times \pi \approx 5832 \times 3.14159 \approx 18328.87 \]
Finally, divide by 3:
\[ V \approx \frac{18328.87}{3} \approx 6109.62 \]
Therefore, the volume of the cone is approximately \( 6109.62 \) cubic miles (cu mi).
### Answer:
**The volume of the cone is approximately 6109.62 cubic miles.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e9d242-cb37-4bc8-a74f-f7cca1efbc15%2Fa4419b47-9920-436d-bf0f-cc10aed63747%2Fog9juhr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Calculating Volume of a Cone**
### Problem Statement:
Find the volume of the cone. Round to the nearest hundredth.
#### Diagram Description:
There is a diagram of a right cone. The height of the cone is labeled as 18 miles (mi), and the radius of the base of the cone is also labeled as 18 miles (mi).
### Solution:
To find the volume \( V \) of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( \pi \) (pi) is approximately 3.14159.
- \( r \) is the radius of the base of the cone.
- \( h \) is the height of the cone.
Given:
- \( r = 18 \) mi
- \( h = 18 \) mi
Substitute the given values into the formula:
\[ V = \frac{1}{3} \pi (18)^2 (18) \]
First, calculate \( r^2 \) (the square of the radius):
\[ 18^2 = 324 \]
Next, multiply this result by the height of the cone:
\[ 324 \times 18 = 5832 \]
Now, multiply by \( \pi \):
\[ 5832 \times \pi \approx 5832 \times 3.14159 \approx 18328.87 \]
Finally, divide by 3:
\[ V \approx \frac{18328.87}{3} \approx 6109.62 \]
Therefore, the volume of the cone is approximately \( 6109.62 \) cubic miles (cu mi).
### Answer:
**The volume of the cone is approximately 6109.62 cubic miles.**
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