Question
Use the image to answer the question.
An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
Responses
47.1 cubic inches
47.1 cubic inches
235.5 cubic inches
235.5 cubic inches
942 cubic inches
942 cubic inches
423.9 cubic inches
423.9 cubic inches
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An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
Responses
47.1 cubic inches
47.1 cubic inches
235.5 cubic inches
235.5 cubic inches
942 cubic inches
942 cubic inches
423.9 cubic inches
423.9 cubic inches
Skip to navigation
Answers
GPT-4o mini
To find the volume of a cone, you can use the formula:
\[
\text{Volume} = \frac{1}{3} \pi r^2 h
\]
Where:
- \( r \) is the radius of the base
- \( h \) is the height of the cone
Given:
- \( r = 9 \) inches
- \( h = 5 \) inches
- Using \( \pi \approx 3.14 \)
Now plug in the values:
\[
\text{Volume} = \frac{1}{3} \times 3.14 \times (9)^2 \times 5
\]
Calculate \( (9)^2 \):
\[
(9)^2 = 81
\]
Now substitute back into the formula:
\[
\text{Volume} = \frac{1}{3} \times 3.14 \times 81 \times 5
\]
Calculate \( 81 \times 5 \):
\[
81 \times 5 = 405
\]
Now substitute that value into the formula:
\[
\text{Volume} = \frac{1}{3} \times 3.14 \times 405
\]
Calculate \( 3.14 \times 405 \):
\[
3.14 \times 405 = 1273.7
\]
Now divide by 3:
\[
\text{Volume} = \frac{1273.7}{3} \approx 424.57
\]
Rounding to one decimal point gives \( 424.6 \), which closely matches the option provided, but let's verify.
The closest option to our calculation is **423.9 cubic inches**, so the correct answer is:
**423.9 cubic inches**.
\[
\text{Volume} = \frac{1}{3} \pi r^2 h
\]
Where:
- \( r \) is the radius of the base
- \( h \) is the height of the cone
Given:
- \( r = 9 \) inches
- \( h = 5 \) inches
- Using \( \pi \approx 3.14 \)
Now plug in the values:
\[
\text{Volume} = \frac{1}{3} \times 3.14 \times (9)^2 \times 5
\]
Calculate \( (9)^2 \):
\[
(9)^2 = 81
\]
Now substitute back into the formula:
\[
\text{Volume} = \frac{1}{3} \times 3.14 \times 81 \times 5
\]
Calculate \( 81 \times 5 \):
\[
81 \times 5 = 405
\]
Now substitute that value into the formula:
\[
\text{Volume} = \frac{1}{3} \times 3.14 \times 405
\]
Calculate \( 3.14 \times 405 \):
\[
3.14 \times 405 = 1273.7
\]
Now divide by 3:
\[
\text{Volume} = \frac{1273.7}{3} \approx 424.57
\]
Rounding to one decimal point gives \( 424.6 \), which closely matches the option provided, but let's verify.
The closest option to our calculation is **423.9 cubic inches**, so the correct answer is:
**423.9 cubic inches**.