Thank you for visiting Find the volume of a cylinder with a diameter of 10 inches and a height of 20 inches A 705 cu in B 6 280. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the volume of a cylinder, we can use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height of the cylinder,
- [tex]\( \pi \)[/tex] is approximately 3.14159.
Let's break it down step-by-step:
1. Determine the radius of the cylinder:
The diameter is given as 10 inches, so the radius is half of the diameter:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ inches}
\][/tex]
2. Use the volume formula:
Substitute the radius and height into the formula:
[tex]\[
V = \pi \times (5 \text{ in})^2 \times 20 \text{ in}
\][/tex]
3. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = 5^2 = 25
\][/tex]
4. Multiply through to find the volume:
[tex]\[
V = \pi \times 25 \times 20
\][/tex]
5. Simplify inside the parentheses:
[tex]\[
V = \pi \times 500
\][/tex]
6. Approximate using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
V \approx 3.14159 \times 500 \approx 1570.8 \text{ cubic inches}
\][/tex]
So, the volume of the cylinder is approximately 1,570 cubic inches. Therefore, the correct option is:
C) 1,570 cu. in.
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height of the cylinder,
- [tex]\( \pi \)[/tex] is approximately 3.14159.
Let's break it down step-by-step:
1. Determine the radius of the cylinder:
The diameter is given as 10 inches, so the radius is half of the diameter:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ inches}
\][/tex]
2. Use the volume formula:
Substitute the radius and height into the formula:
[tex]\[
V = \pi \times (5 \text{ in})^2 \times 20 \text{ in}
\][/tex]
3. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = 5^2 = 25
\][/tex]
4. Multiply through to find the volume:
[tex]\[
V = \pi \times 25 \times 20
\][/tex]
5. Simplify inside the parentheses:
[tex]\[
V = \pi \times 500
\][/tex]
6. Approximate using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
V \approx 3.14159 \times 500 \approx 1570.8 \text{ cubic inches}
\][/tex]
So, the volume of the cylinder is approximately 1,570 cubic inches. Therefore, the correct option is:
C) 1,570 cu. in.
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Rewritten by : Jeany
