Find the volume of the solid. Round your answer to the nearest tenth or write in terms of pi. Hint: Volume of a cylinder: V = Bh, Volume of a sphere: V = 4/3TTP 15. r = 5 in, h = 8 in 16. r = 6 cm
Find the volume of the solid. Round your answer to the nearest tenth or write in terms of pi. Hint: Volume of a cylinder: V = Bh, Volume of a sphere: V = 4/3TTP 15. r = 5 in, h = 8 in 16. r = 6 cm
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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find the volume of the solid. Round the answer to the nearest tenth or write in terms of pi. See image attached.
![### Calculating the Volume of Solids
**Objective:** Determine the volume of the given solid shapes. Round your answer to the nearest tenth or express the answer in terms of π.
**Equations:**
- **Volume of a Cylinder:** \( V = Bh \)
- **Volume of a Sphere:** \( V = \frac{4}{3} \pi r^3 \)
where:
- \( B \) is the area of the base of the cylinder (\( B = \pi r^2 \))
- \( h \) is the height of the cylinder
- \( r \) is the radius of the base or the radius of the sphere.
**Examples:**
**15. Volume of a Cylinder**
- **Given:**
- Radius (\( r \)) = 5 inches
- Height (\( h \)) = 8 inches
- **Calculation:**
1. Find the area of the base \( B \):
\[
B = \pi r^2 = \pi (5)^2 = 25\pi \text{ square inches}
\]
2. Calculate the Volume \( V \):
\[
V = Bh = 25\pi \times 8 = 200\pi \text{ cubic inches} \approx 628.3 \text{ cubic inches}
\]
- **Diagram:**
- A blue cylinder with a radius of 5 inches and a height of 8 inches.
**16. Volume of a Sphere**
- **Given:**
- Radius (\( r \)) = 6 cm
- **Calculation:**
1. Calculate the volume \( V \):
\[
V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) = 288\pi \text{ cubic centimeters} \approx 904.8 \text{ cubic centimeters}
\]
- **Diagram:**
- A green sphere with a radius of 6 cm.
By understanding and applying these volume formulas, students can efficiently solve problems related to the volume of cylinders and spheres.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64fa9c8f-08da-4669-be68-ade6ed0b5d78%2Fd2323d39-7db8-4ab2-a7ef-0484393f5e1c%2F9nrsgnj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Volume of Solids
**Objective:** Determine the volume of the given solid shapes. Round your answer to the nearest tenth or express the answer in terms of π.
**Equations:**
- **Volume of a Cylinder:** \( V = Bh \)
- **Volume of a Sphere:** \( V = \frac{4}{3} \pi r^3 \)
where:
- \( B \) is the area of the base of the cylinder (\( B = \pi r^2 \))
- \( h \) is the height of the cylinder
- \( r \) is the radius of the base or the radius of the sphere.
**Examples:**
**15. Volume of a Cylinder**
- **Given:**
- Radius (\( r \)) = 5 inches
- Height (\( h \)) = 8 inches
- **Calculation:**
1. Find the area of the base \( B \):
\[
B = \pi r^2 = \pi (5)^2 = 25\pi \text{ square inches}
\]
2. Calculate the Volume \( V \):
\[
V = Bh = 25\pi \times 8 = 200\pi \text{ cubic inches} \approx 628.3 \text{ cubic inches}
\]
- **Diagram:**
- A blue cylinder with a radius of 5 inches and a height of 8 inches.
**16. Volume of a Sphere**
- **Given:**
- Radius (\( r \)) = 6 cm
- **Calculation:**
1. Calculate the volume \( V \):
\[
V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) = 288\pi \text{ cubic centimeters} \approx 904.8 \text{ cubic centimeters}
\]
- **Diagram:**
- A green sphere with a radius of 6 cm.
By understanding and applying these volume formulas, students can efficiently solve problems related to the volume of cylinders and spheres.
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