To find the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) (pi) is approximately 3.14.
From the information provided:
- The diameter of the cylinder is 15 cm, which means the radius (\( r \)) is half of that:
\[ r = \frac{15 \text{ cm}}{2} = 7.5 \text{ cm} \]
- The height (\( h \)) of the cylinder is 5 cm.
Now plug in the values into the volume formula:
\[ V = 3.14 \times (7.5 \text{ cm})^2 \times 5 \text{ cm} \]
First, calculate \( (7.5 \text{ cm})^2 \):
\[ (7.5 \text{ cm})^2 = 56.25 \text{ cm}^2 \]
Now substitute that back into the volume formula:
\[ V = 3.14 \times 56.25 \text{ cm}^2 \times 5 \text{ cm} \]
Now calculate \( 3.14 \times 56.25 \):
\[ 3.14 \times 56.25 = 176.625 \]
Next, multiply that result by 5 cm:
\[ V = 176.625 \times 5 = 883.125 \text{ cm}^3 \]
It looks like I made an error earlier, let's recalculate:
Correct final calculation:
\[ 3.14 \times 56.25 = 176.625 \] \[ 176.625 \times 5 = 883.125 \]
Now returning to the possible responses you provided, the correct volume for the cylinder from the calculations we've done seems to be incorrect since 883.125 is not included in the possible responses.
Looking at the options listed:
- 1177.5 cubic centimeters
- 235.5 cubic centimeters
- 471 square centimeters
- 1177.5 centimeters
None of these match our calculated volume.
Re-evaluating:
Looks like the dimensions or possible options should be checked again or the methodology has to be reassessed in light of existing calculations.
You might want to consider if additional clarifications are needed for the options or if details may have been missed in either model dimensions or computations.
If we assumed either height or radius was misstated or verify underlying assumptions could put us in the right path.
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