Question

Kala’s company makes solid metal balls for various industrial uses. A customer wants aluminum balls that have a diameter of 6 in. If Kala must make 70 of those balls, how much aluminum will she need?

Answer 1

7,912.8 inch³ of aluminum is needed to make 70 metal balls.

Explanation:

Step 1:

The area of a sphere is calculated by multiplying
`(4)/(3)` with π and the cube of the radius (r³).

In the given problem, the diameter is 6 inches. So the radius of the spheres is 3 inches.

The volume of a sphere,
`V = (4)/(3) \pi r^(3) .`

So if r = 3 inches and π = 3.14,

`V = (4)/(3) (3.14) (3^(3)) = 113.04` cubic inches.

So for a single aluminum ball, 113.04 inch³ of aluminum is needed.

Step 2:

If 113.04 inch³ of aluminum is used for 1 ball, then we multiply 70 with this value to determine the aluminum needed for 70 such balls.

The aluminum needed for 70 metal balls
`= 70(113.04) = 7,912.8` inch³.

So 7,912.8 inch³ of aluminum is needed to make 70 metal balls.