Question
Question
Use the image to answer the question.
An inverted cone of height 6 inches and radius 2 inches is shown.
Anders finds the volume of the cone in the image. What is the volume of this cone in cubic inches? Use 3.14 to represent pi and round the volume to the nearest cubic inch.
(8 points)
Responses
13 cubic inches
13 cubic inches
75 cubic inches
75 cubic inches
24 cubic inches
24 cubic inches
25 cubic inches
25 cubic inches
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Use the image to answer the question.
An inverted cone of height 6 inches and radius 2 inches is shown.
Anders finds the volume of the cone in the image. What is the volume of this cone in cubic inches? Use 3.14 to represent pi and round the volume to the nearest cubic inch.
(8 points)
Responses
13 cubic inches
13 cubic inches
75 cubic inches
75 cubic inches
24 cubic inches
24 cubic inches
25 cubic inches
25 cubic inches
Skip to navigation
Answers
GPT-4o mini
To find the volume of the inverted cone, we can use the formula for the volume of a cone, which is:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.
Given the height \(h = 6\) inches and the radius \(r = 2\) inches, we can substitute these values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6
\]
Calculating \( (2)^2 \):
\[
(2)^2 = 4
\]
Now substitute this value back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
Now calculate \(4 \times 6\):
\[
4 \times 6 = 24
\]
Now substitute this into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
Now multiply \(3.14\) by \(24\):
\[
3.14 \times 24 = 75.36
\]
Now divide by \(3\):
\[
V = \frac{75.36}{3} = 25.12
\]
Rounding \(25.12\) to the nearest cubic inch gives us \(25\).
Therefore, the volume of the cone is approximately **25 cubic inches**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.
Given the height \(h = 6\) inches and the radius \(r = 2\) inches, we can substitute these values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6
\]
Calculating \( (2)^2 \):
\[
(2)^2 = 4
\]
Now substitute this value back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
Now calculate \(4 \times 6\):
\[
4 \times 6 = 24
\]
Now substitute this into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
Now multiply \(3.14\) by \(24\):
\[
3.14 \times 24 = 75.36
\]
Now divide by \(3\):
\[
V = \frac{75.36}{3} = 25.12
\]
Rounding \(25.12\) to the nearest cubic inch gives us \(25\).
Therefore, the volume of the cone is approximately **25 cubic inches**.