https://file.aiquickdraw.com/mathbot/file/1721319304641nzau2qjc.png

What is the volume of each hemisphere in the picture below? (Use 3.14 for 𝜋)

To find the volume of each hemisphere in the image, we first need to calculate the volume of the whole sphere and then divide it by two.

The formula for the volume of a sphere is:

\[ V = \frac{4}{3} \pi r^3 \]

Given:
- The diameter of the sphere is 3.7 inches.
- Therefore, the radius \( r \) is half of the diameter: \( r = \frac{3.7}{2} = 1.85 \) inches.

Using the approximation \( \pi \approx 3.14 \):

\[ V = \frac{4}{3} \times 3.14 \times (1.85)^3 \]

First, we calculate \( 1.85^3 \):

\[ 1.85^3 = 1.85 \times 1.85 \times 1.85 = 6.328625 \]

Next, we substitute this back into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 6.328625 \]
\[ V = \frac{4}{3} \times 19.872465 \]
\[ V = 4 \times 6.624155 \]
\[ V = 26.49662 \text{ cubic inches} \]

Since we need the volume of each hemisphere, we divide this result by 2:

\[ V_{\text{hemisphere}} = \frac{26.49662}{2} \approx 13.24831 \text{ cubic inches} \]

Thus, the volume of each hemisphere is approximately \( 13.24831 \) cubic inches.

Would you like any more details or have any questions?

Here are some related questions you might want to ask:
1. How do you derive the formula for the volume of a sphere?
2. What is the surface area of the hemisphere?
3. How do you calculate the volume of a cylinder?
4. What is the relationship between the volume of a cone and a cylinder?
5. How do you find the volume of an irregularly shaped object?

**Tip:** Always double-check the units of measurement in a problem to ensure accuracy in your calculations.

Learn how to calculate the volume of each hemisphere from a sphere with a diameter of 3.7 inches using the formula for the volume of a sphere and hemisphere. Step-by-step solution provided with calculations using π = 3.14.

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