To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
In your case, you provided the dimensions: the height \( h = 6 \) inches and the diameter of the base is \( 2 \) inches. First, we need to find the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{2}{2} = 1 \text{ inch} \]
Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (1^2) \times 6 \]
Calculating this step by step:
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Calculate \( r^2 \): \[ r^2 = 1^2 = 1 \]
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Substitute into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 1 \times 6 \]
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Multiply: \[ V = \frac{1}{3} \times 3.14 \times 6 = \frac{18.84}{3} = 6.28 \]
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Round to the nearest cubic inch: \[ V \approx 6 \text{ cubic inches} \]
Since none of the answer choices (13, 24, 75, 25 cubic inches) matches this value, please double-check the dimensions or options given. Based on the provided dimensions of a cone with a height of 6 inches and a diameter of 2 inches, the volume is approximately 6 cubic inches.
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