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
![Title: Calculating the Volume of a Basketball
---
**Problem Statement:**
*11. Find the VOLUME of my basketball with a radius of 4.75 inches.*
---
**Explanation:**
To find the volume of a basketball, which is a sphere, you need to use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( r \) is the radius, and \( \pi \) (pi) is approximately 3.14159.
Given:
Radius (\( r \)) = 4.75 inches
Plugging the radius into the formula:
\[ V = \frac{4}{3} \times 3.14159 \times (4.75)^3 \]
Let's calculate this step by step:
1. Calculate \( 4.75^3 \):
\[ 4.75^3 = 4.75 \times 4.75 \times 4.75 = 107.171875 \]
2. Next, multiply this result by \( \pi \) (approximately 3.14159):
\[ 107.171875 \times 3.14159 \approx 336.256 \]
3. Finally, multiply by \( \frac{4}{3} \):
\[ \frac{4}{3} \times 336.256 \approx 448.341 \]
So, the volume of the basketball is approximately 448.34 cubic inches.
---
**Visual Description:**
The image shows an orange basketball with black lines, typical of professional basketballs. The texture is bumpy, conducive for gripping. This visual helps students connect the given problem with a real-world object.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbddcb8c-1b25-4c9a-b40d-a5fe79d16dfd%2F6623652e-d332-4824-8661-f9131ff2c4cf%2Ftmkq5rm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Calculating the Volume of a Basketball
---
**Problem Statement:**
*11. Find the VOLUME of my basketball with a radius of 4.75 inches.*
---
**Explanation:**
To find the volume of a basketball, which is a sphere, you need to use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( r \) is the radius, and \( \pi \) (pi) is approximately 3.14159.
Given:
Radius (\( r \)) = 4.75 inches
Plugging the radius into the formula:
\[ V = \frac{4}{3} \times 3.14159 \times (4.75)^3 \]
Let's calculate this step by step:
1. Calculate \( 4.75^3 \):
\[ 4.75^3 = 4.75 \times 4.75 \times 4.75 = 107.171875 \]
2. Next, multiply this result by \( \pi \) (approximately 3.14159):
\[ 107.171875 \times 3.14159 \approx 336.256 \]
3. Finally, multiply by \( \frac{4}{3} \):
\[ \frac{4}{3} \times 336.256 \approx 448.341 \]
So, the volume of the basketball is approximately 448.34 cubic inches.
---
**Visual Description:**
The image shows an orange basketball with black lines, typical of professional basketballs. The texture is bumpy, conducive for gripping. This visual helps students connect the given problem with a real-world object.
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