Respuesta :
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
[tex]\text {Volume of ball }=\text { Volume of sphere }=\frac{4}{3} \pi r^{3}[/tex]
Where "r" is the raius of ball
Given that radius of required ball = 7.5 inches
[tex]\text { So, volume of ball of radius } 7.5 \text { inches }=\frac{4}{3} \pi \times 7.5^{3}[/tex]
[tex]=\frac{4}{3} \times 3.14 \times 321.875=1347.5833 \text { cubic inches }[/tex]
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:
[tex]=0.12 \times 1347.5833=\$ 161.71[/tex]
