Question about math geometry (its difficultish 10 grade math)

4) You’re a hip new fashion designer for Coach and are in the process of designing a new handbag. It’s to be shaped like a hemisphere with a radius of 4 inches. What is the surface area and volume of this new handbag? Give exact answers.





Surface Area = ____________________
Volume = ____________________

5) Your boss has decided to give you approval for production of your newly designed handbag in problem 4. The leather for these bags will cost $240 for a 50 square foot piece. If you plan on producing 1000 of these handbags, what will be the total cost for the leather?





Total Cost of Leather = ____________________

4)
The formula for surafce area of a sphere is SA=4(pi)r^2
Since we want surface area of a hemisphere (half a sphere) then formula is changed to:
SA=(4πr^2)/2

So now if we input the numbers:
SA=(4π4^2)/2
=(4π16)/2
=32π in^2

Formula for volume of sphere is V=(4/3)πr^3
Since volume for hemisphere is needed then formula becomes

V=((4/3)πr^3)/2

So now if we input the numbers:
V=((4/3)π4^3)/2
=((4/3)π64)2
=(128/3)π in^3



5)
Total area of leather needed:

1000(32π)=100530.9649 square inches

Convert to square feet:

100530.9649/144=698.1317008 square feet

Then divide by the 50 square foot piece to get the total pieces needed:

698.1317008/50=13.96263402

Then multiply by the cost of one piece of leather:

13.96263402(240)=$3351.03

The total cost of the leather will be $3351.03