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.

Step-by-step explanation:

Step 1:

The area of a sphere is calculated by multiplying $\frac{4}{3}$ 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,$V = \frac{4}{3} \pi r^{3} .$

So if r = 3 inches and π = 3.14,  

$V = \frac{4}{3} (3.14) (3^{3}) = 113.04$ 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.