Question

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

Answer 1

The formula for the volume of a sphere is
`\frac{4}3\pi r^3`.

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.


`V=\frac{4}3\pi 5^3 \\\\ 5^3=5*5*5=125\\V=\frac{4}3\pi 125 \\\\ \frac{4}3*125\approx166.667 \\ V\approx166.667\pi \\\\ \pi\approx3.14 \\ V\approx166.667*3.14\approx\boxed{523.3\ in^3}`

Answer 2

Volume of sphere(V) is given by:

`V =(4)/(3) \pi r^3` ....[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:

`\text{Diameter}(d) = 2r`

`10 = 2r`

Divide both sides by 2 we get;

`5 = r`

or

r = 5 inches

Substitute in [1] we get;

`V =(4)/(3) \pi 5^3`

Use
`\pi = 3.14`

then;

`V = (4)/(3) \cdot 3.14 \cdot 125`

Simplify:

⇒ V = 523.333332 cubic inches

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