Question

question
what is the volume of a hemisphere with a radius of 30.8 cm, rounded to the nearest tenth of a cubic centimeter?

Explanation:

Step1: Recall the formula for the volume of a hemisphere

The volume \( V \) of a hemisphere is given by the formula \( V=\frac{2}{3}\pi r^{3} \), where \( r \) is the radius of the hemisphere.

Step2: Substitute the given radius into the formula

We are given that \( r = 30.8\space\text{cm} \). Substitute \( r = 30.8 \) into the formula:

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Step3: Calculate the numerical value

First, calculate \( \frac{2}{3}\times29376.128=\frac{58752.256}{3} = 19584.0853\overline{3} \)
Then multiply by \( \pi \) (using \( \pi\approx3.14159 \)):
\( V\approx19584.0853\overline{3}\times3.14159\approx61529.7 \) (rounded to the nearest tenth)

Answer:

The volume of the hemisphere is approximately \( 61529.7\space\text{cubic centimeters} \)