To calculate the volume of a sphere, we can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
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First, we need to find the radius from the diameter: \[ \text{Diameter} = 15 , \text{cm} \implies \text{Radius} = \frac{\text{Diameter}}{2} = \frac{15}{2} = 7.5 , \text{cm} \]
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Next, we can plug the radius into the volume formula using \( \pi \approx 3.14 \): \[ V = \frac{4}{3} \times 3.14 \times (7.5)^3 \]
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Calculate \( (7.5)^3 \): \[ (7.5)^3 = 7.5 \times 7.5 \times 7.5 = 421.875 , \text{cm}^3 \]
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Now substitute back into the volume formula: \[ V = \frac{4}{3} \times 3.14 \times 421.875 \]
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Calculate \( \frac{4}{3} \times 3.14 \): \[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
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Now multiply by \( 421.875 \): \[ V \approx 4.18667 \times 421.875 \approx 1767.145 \]
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Rounding to the nearest tenth gives: \[ V \approx 1767.1 , \text{cm}^3 \]
It appears there was some mistake in the unit. The volume indicated is in cubic centimeters, not cubic meters.
However, examining your options—there does not seem to be a match directly; thus, there may have been an assumption of volume unit. Nonetheless, based on our calculation, the closest answer to 1767.1 is 1,766.3 cubic meters, assuming a misstatement in units.
To clarify, the answer selected considering units should account for cubic centimeters, and the needed response with regard to the potential options provided must be asserted to 1,766.3 cubic meters.