Question
Volume of Cones Practice
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Question
A coffee maker has a cone-shaped container to hold the coffee grounds. The radius of the container is 3 inches and the height is 7 inches. What is the volume, in cubic inches, of coffee grounds the container can hold? Round your answer to the nearest hundredth and use 3.14 for π
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Answers
GPT-4o mini
To find the volume \( V \) of a cone, you can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
In this case:
- \( r = 3 \) inches,
- \( h = 7 \) inches,
- \( \pi \approx 3.14 \).
Now, substitute the values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7
\]
Calculating \( (3)^2 \):
\[
(3)^2 = 9
\]
Now substitute this value:
\[
V = \frac{1}{3} \times 3.14 \times 9 \times 7
\]
Calculate \( 9 \times 7 = 63 \):
\[
V = \frac{1}{3} \times 3.14 \times 63
\]
Now calculate \( 3.14 \times 63 \):
\[
3.14 \times 63 = 197.82
\]
Now divide by 3:
\[
V = \frac{197.82}{3} \approx 65.94
\]
Therefore, the volume of the cone-shaped container is approximately
\[
\boxed{65.94} \text{ cubic inches.}
\]
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
In this case:
- \( r = 3 \) inches,
- \( h = 7 \) inches,
- \( \pi \approx 3.14 \).
Now, substitute the values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7
\]
Calculating \( (3)^2 \):
\[
(3)^2 = 9
\]
Now substitute this value:
\[
V = \frac{1}{3} \times 3.14 \times 9 \times 7
\]
Calculate \( 9 \times 7 = 63 \):
\[
V = \frac{1}{3} \times 3.14 \times 63
\]
Now calculate \( 3.14 \times 63 \):
\[
3.14 \times 63 = 197.82
\]
Now divide by 3:
\[
V = \frac{197.82}{3} \approx 65.94
\]
Therefore, the volume of the cone-shaped container is approximately
\[
\boxed{65.94} \text{ cubic inches.}
\]