The volume of a hemisphere is `"718.67 cm"^3.` Find its diameter (in cm).

Options

A. 7
B. 28
C. 14
D. 21

Answer

To find the diameter of a hemisphere given its volume, we can follow these steps:

### Step 1: Understand the formula for the volume of a hemisphere
The formula for the volume \( V \) of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
where \( r \) is the radius of the hemisphere.

### Step 2: Set up the equation with the given volume
We know the volume of the hemisphere is \( 718.67 \, \text{cm}^3 \). We can set up the equation:
\[ \frac{2}{3} \pi r^3 = 718.67 \]

### Step 3: Solve for \( r^3 \)
To isolate \( r^3 \), we can multiply both sides of the equation by \( \frac{3}{2} \):
\[ \pi r^3 = 718.67 \times \frac{3}{2} \]
Calculating the right side:
\[ \pi r^3 = 718.67 \times 1.5 = 1078.005 \]

Next, we divide both sides by \( \pi \):
\[ r^3 = \frac{1078.005}{\pi} \]
Using \( \pi \approx 3.14 \):
\[ r^3 \approx \frac{1078.005}{3.14} \approx 343.49 \]

### Step 4: Calculate the radius \( r \)
Now we take the cube root of both sides to find \( r \):
\[ r \approx \sqrt[3]{343.49} \approx 7 \, \text{cm} \]

### Step 5: Find the diameter
The diameter \( d \) of the hemisphere is twice the radius:
\[ d = 2r = 2 \times 7 = 14 \, \text{cm} \]

### Conclusion
The diameter of the hemisphere is \( 14 \, \text{cm} \).

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