Questions: Find the volume of the hemisphere. Use 3.14 for π. The volume is in ^3 (Round to the nearest tenth.)

Transcript text: Find the volume of the hemisphere. Use 3.14 for $\pi$. The volume is $\square$ in $^{3}$ (Round to the nearest tenth.)

Solution

Solution Steps

Step 1: Identify the formula for the volume of a hemisphere

The volume $ V $ of a hemisphere is given by the formula: \[ V = \frac{2}{3} \pi r^3 \]

Step 2: Determine the radius

From the image, the diameter of the hemisphere is 9 meters. Therefore, the radius $ r $ is half of the diameter: \[ r = \frac{9}{2} = 4.5 \, \text{m} \]

Step 3: Substitute the values into the formula

Using $ \pi = 3.14 $ and $ r = 4.5 $: \[ V = \frac{2}{3} \times 3.14 \times (4.5)^3 \]

Step 4: Calculate the volume

First, calculate $ (4.5)^3 $: \[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 91.125 \]

Next, substitute this value back into the formula: \[ V = \frac{2}{3} \times 3.14 \times 91.125 \] \[ V = \frac{2}{3} \times 286.1325 \] \[ V = 190.755 \]