Cole is building a model rocket in science class. He selects the rocket parts from a set of solid cylinders and cones made from metal. Cole wants to build a rocket with the dimensions shown. For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. Will Cole’s rocket meet the requirement for launch?

Part A
What will be the total length of the assembled rocket? Explain how you found your answer.
Part B
What is the approximate volume of the rocket. Use 3.14 for π. Explain.
Part C
If Cole’s rocket parts are made of aluminum weighing 0.006 pound per cubic centimeter, will Cole be able to launch his rocket? Explain.

A.

30 since 25 + 5 = 30

The maximum lift-off weight of each rocket is 10 pounds thus, Cole’s rocket doesn't meet the requirement for launch.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2} h[/tex]

Part A

The total length of the assembled rocket will be the length of the cone and the cylinder.

Height of the cone

[tex]\sqrt{l^{2} -r^{2} } \\\\\sqrt{5^{2} -4^{2} } \\[/tex] = 3 cm

The total length of the assembled rocket  = 25 + 3 = 28cm

Part B

The volume of the rocket is the combined volume of the cone and cylinder.

=  [tex]\pi r^{2} h[/tex] + 1/3[tex]\pi r^{2} h[/tex]

= 4/3 [tex]\pi r^{2} h[/tex]

=  4/3 × 3.14 × 16 × 28

= 1875.62 cubic cm

To convert cm into pound

1875.62 cubic cm = 4.135 pound

Part C

If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.

Then 1875.62 cubic cm × 0.006

= 11.253

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

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