To find the volume \( V \) of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- \( r = 8.7 \) centimeters,
- \( h = 27.8 \) centimeters,
- \( \pi \approx 3.14 \).
Now, let's plug in the values:
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Calculate \( r^2 \): \[ r^2 = (8.7)^2 = 75.69 \]
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Now substitute the values into the volume formula: \[ V = 3.14 \times 75.69 \times 27.8 \]
First, calculate \( 3.14 \times 75.69 \): \[ 3.14 \times 75.69 \approx 237.2726 \]
Next, multiply by the height \( h \): \[ V \approx 237.2726 \times 27.8 \approx 6598.99 \]
Finally, rounding to the nearest tenth, the volume of the display stand is approximately: \[ \boxed{6599.0} \text{ cubic centimeters.} \]