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.
Answers
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.
What is the volume of a cylinder?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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Answer:
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