An employee at a fireworks company is designing a rocket. The rocket will consist of a cardboard circular cylinder with a height that is seven times as large as the radius. On top of the cylinder will be a cone with a height of 5 in. and a radius equal to the radius of the base as shown in the figure. If the company wants to fill the cone and the cylinder with a total of 204 in.^3 of powder, then what should be the radius of the cylinder? Note that the volume of a right circular cylinder with radius r and height h is and the volume of a cone with a base of radius r and height h is .

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xero099 xero099 · Answer 1 · 2022-07-22T00:34:26+02:00

The radius of the cylinder should be approximately 2.040 inches long.

The volume required to store the powder is the sum of the volumes of the cylinder and the cone, whose expression is in this case:

204 in³ = (π/3) · r² · (4 in) + π · r² · h

204 in³ = (4/3 + h) · π · r²

204 in³ = (4/3 + 7 · r) · π · r²

204 = (4π/3) · r² + 7π · r³

7π · r³ + (4π/3) · r² - 204 = 0

The positive roots of the cubic equation are:

r ≈ 2.040 in

The radius of the cylinder should be approximately 2.040 inches long.

To learn more on volumes: https://brainly.com/question/1578538

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