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 }=(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 }=(4)/(3) \pi * 7.5^(3)`

`=(4)/(3) * 3.14 * 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 * 1347.5833=\$ 161.71`