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.
(1 point)
Responses
24 cubic inches
24 cubic inches
25 cubic inches
25 cubic inches
13 cubic inches
13 cubic inches
75 cubic inches
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.
(1 point)
Responses
24 cubic inches
24 cubic inches
25 cubic inches
25 cubic inches
13 cubic inches
13 cubic inches
75 cubic inches
Answers
GPT-4o mini
To find the volume of a cone, we can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cone.
Given that the radius \( r = 2 \) inches and the height \( h = 6 \) inches, we can substitute these values into the formula. Using \( \pi \approx 3.14 \), we have:
\[
V = \frac{1}{3} \times 3.14 \times (2^2) \times 6
\]
First, calculate \( 2^2 \):
\[
2^2 = 4
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
Next, calculate \( 4 \times 6 = 24 \):
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
Now, multiply \( 3.14 \times 24 \):
\[
3.14 \times 24 = 75.36
\]
Now take one-third of that:
\[
V = \frac{75.36}{3} = 25.12
\]
Finally, rounding to the nearest cubic inch, we find:
\[
V \approx 25 \text{ cubic inches}
\]
Thus, the volume of the cone is **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 of the cone.
Given that the radius \( r = 2 \) inches and the height \( h = 6 \) inches, we can substitute these values into the formula. Using \( \pi \approx 3.14 \), we have:
\[
V = \frac{1}{3} \times 3.14 \times (2^2) \times 6
\]
First, calculate \( 2^2 \):
\[
2^2 = 4
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
Next, calculate \( 4 \times 6 = 24 \):
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
Now, multiply \( 3.14 \times 24 \):
\[
3.14 \times 24 = 75.36
\]
Now take one-third of that:
\[
V = \frac{75.36}{3} = 25.12
\]
Finally, rounding to the nearest cubic inch, we find:
\[
V \approx 25 \text{ cubic inches}
\]
Thus, the volume of the cone is **25 cubic inches**.