Question

PLEASE ANSWER THIS . Goran's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make aluminum balls that have a radius of 7.5 . If aluminum costs $0.12 per in³, how much will the aluminum cost to make one ball? Use 3.14 for π , and do not round your answer.

Answer 1

Cost of aluminum required to make a ball of radius 7.5 inches is $ 161.71

Solution:

Given that  

Goran's company makes solid balls out of scrap metal for various industrial uses.

For one project, he must make aluminum balls that have a radius of 7.5 inches.

Cost of aluminum = $0.12 per cubic inches

Need to determine cost of aluminum to make one ball.

Lets first calculate the volume of one ball

As shape of the ball is sphere , we can use volume of sphere formula

$\text {Volume of ball }=\text { Volume of sphere }=\frac{4}{3} \pi r^{3}$

Where "r" is the raius of ball

Given that radius of required ball = 7.5 inches

$\text { So, volume of ball of radius } 7.5 \text { inches }=\frac{4}{3} \pi \times 7.5^{3}$

$=\frac{4}{3} \times 3.14 \times 321.875=1347.5833 \text { cubic inches }$

So quantity of aluminum required is same as volume of ball = 1347.5833 cubic inches  

Cost of aluminum for 1 cubic inch = $0.12

So cost of aluminum required to make a ball of aluminium of 1347.5833 cubic inches is given as:

$=0.12 \times 1347.5833=\ 161.71$