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, and \( h \) is the height.
From the information provided:
- The diameter of the cone is 6 inches, which gives a radius of:
\[ r = \frac{diameter}{2} = \frac{6 \text{ in}}{2} = 3 \text{ in} \]
- The height \( h \) of the cone is 2 inches.
Now we can substitute the radius and height into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot (3)^2 \cdot 2 \]
Calculating step by step:
- Calculate \( (3)^2 = 9 \).
- Multiply by the height:
\[ 9 \cdot 2 = 18 \]
- Now multiply by \( \pi \) (using 3.14):
\[ 3.14 \cdot 18 = 56.52 \]
- Finally, multiply by \( \frac{1}{3} \):
\[ V = \frac{56.52}{3} \approx 18.84 \]
Rounding to the nearest cubic inch gives:
\[ V \approx 19 \text{ cubic inches} \]
However, the given answer choices are:
- 13 cubic inches
- 24 cubic inches
- 75 cubic inches
- 25 cubic inches
Since 19 cubic inches is not an option and there's a possibility of errors in rounding or initial data interpretation, let's check if we could have done anything differently with the calculations or assumptions made regarding measurements. The provided volume options suggest the cone’s dimensions may have been misinterpreted.
Please verify the dimensions or provide more context to arrive at the correct answer. If the height or radius were different, the volume would vary significantly.
11 answers