Just need some minor help here AND someone to check my thinking.

Here's the problem:

What is the volume of the following submarine model?

WHAT I KNOW:

Front front rounded part = radius of 3 inch/ length (height) of 3 inch

cylinder body = radius of 3 inch/ length (height) of 12 inches

tail cone part = radius of 3 inches/ length (height) of 4 inches

volume formula for front rounded part = hemisphere = volume of sphere/ 2 = 4/3 * pi * r (cubed)/2

v sphere = 4/3 * 3.14159 *3 (cubed)

v sphere = 1.33333 * 3.14159 * 27

v sphere = 113.09 inch (squared)

v hemisphere = 113.09 inch/2 = 56.545 inch (squared)

volume formula for cylinder body = pi * r (squared) * height

v cylinder = 3.14159 * 3 (squared) * 12

v cylinder = 3.14159 * 9 * 12

v cylinder = 339.2917 inch (cubed)

volume formula for tail cone = 1/3 * pi * r (squared) * Height

v cone = 1/3 * 3.14159 * 3 (squared) * 4

v cone = .33333 * 3.14159 * 9 * 4

v cone = 37.699 inches (cubed)

TOTAL volume of the mini sub = volume of hemisphere + volume of cylinder + volume of tail cone

113.09 + 339.2917 + 37.699 = 490.08 inches

HERE'S QUESTION ONE.....is the answer in cubic inches OR square inches? AND are my calculations correct?

HERE'S QUESTION TWO .....If one inch of the model represents 20 feet in the actual sub, what is the volume of the actual sub?

I believe that this is a proportion problem. Height of hemisphere = 3 in/ height of cylinder = 12 inches/ height of cone = 4 inches.

Total height of model = 19 inches. Total volume of model = 490.08

19 inches * 20 feet = 380 feet (actual sub length)

490.08/ 19 inches = 25.79 volume per inch

25.79 * 12 = 309.48 volume per foot

309.48 * 380 = 117,602 total volume (actual sub)

CORRECT THINKING?

WRONG?

Pls comment and advise.

Thank you!

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