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To calculate the total amount of helium that the sphere-shaped balloon will hold, you can use the formula for the volume of a sphere. The volume of a sphere is given by the formula:
\[ V = \frac{4}{3} \times \pi \times r^3 \]
Where:
- \( V \) is the volume of the sphere.
- \( \pi \) is a constant (approximately 3.14159).
- \( r \) is the radius of the sphere.
Given that the diameter of the balloon is 8 inches, you first need to find the radius by dividing the diameter by 2:
\[ r = \frac{8}{2} = 4 \text{ inches} \]
Now, plug the radius into the volume formula:
\[ V = \frac{4}{3} \times \pi \times (4)^3 \]
\[ V = \frac{4}{3} \times 3.14159 \times 64 \]
\[ V = \frac{4}{3} \times 200.96 \]
\[ V ≈ 268.08 \text{ cubic inches} \]
Therefore, to the nearest tenth, the balloon will hold approximately 268.1 cubic inches of helium.
