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The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14 for PI. Round to the nearest tenth of a cubic inch.

Recall the formula Sphere=4/3 PIr^3

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The formula for the volume of a sphere is [tex]\frac{4}3\pi r^3[/tex].

Our diameter is 10 inches. Since the radius is always half the diameter, the radius must be 5 inches. We can use this value to find the volume.

[tex]V=\frac{4}3\pi 5^3 \\\\ 5^3=5\times5\times5=125\\V=\frac{4}3\pi 125 \\\\ \frac{4}3\times125\approx166.667 \\ V\approx166.667\pi \\\\ \pi\approx3.14 \\ V\approx166.667\times3.14\approx\boxed{523.3\ in^3}[/tex]

Answer:

Volume of sphere(V) is given by:

[tex]V =\frac{4}{3} \pi r^3[/tex]          ....[1]

where

r is the radius of the sphere.

As per the statement:

The diameter of a beach ball is 10 inches.

We know that:

[tex]\text{Diameter}(d) = 2r[/tex]

[tex]10 = 2r[/tex]

Divide both sides by 2 we get;

[tex]5 = r[/tex]

or

r = 5  inches

Substitute in [1] we get;

[tex]V =\frac{4}{3} \pi 5^3[/tex]

Use [tex]\pi = 3.14[/tex]

then;

[tex]V = \frac{4}{3} \cdot 3.14 \cdot 125[/tex]

Simplify:

⇒ V = 523.333332 cubic inches

Therefore, the volume of beach ball to the nearest tenth of a cubic is, 523.3 cubic inches

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