Gage is building a model rocket for a science fair project. He attaches a nosecone to a cylindrical body to form the rocket's fuselage. The rocket has a diameter of 4 inches and a total height (including the nosecone) of 2 feet 5 inches. The nosecone is 7 inches tall. What is the volume of the rocket?

305.78 in2

Step-by-step explanation:

The rocket has two parts: one is a cylinder and the other is a cone.

To find the total volume of the rocket, we need to find firstly the volume of each part.

The cylinder has a radius of 2 inches and a height of 2*12 + 5 - 7 = 22 inches, so its volume is:

V1 = pi * r^2 * h = pi * 2^2 * 22 = 276.46 in2

The cone has a radius of 2 inches and a height of 7 inches, so its volume is:

V2 = (1/3) * pi * r^2 * h = (1/3) * pi * 2^2 * 7 = 29.32 in2

Then, we have that the volume of the rocket is:

V = V1 + V2 = 276.46 + 29.32 = 305.78 in2

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step-by-step explanation:

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