Question

An aerospace engineer is designing a model of a portion of a new telescope, a cylinder with a cone cut-out as shown below. What is the total volume of the materials used to make the new telescope piece?

Answer 1

See explanation

Explanation:

The question is incomplete, as the required figure is not attached to the question.

From the question, we can deduce that the telescope is a composite figure made from a cone and a cylinder.

To get the volume of the materials used, you have to calculate the volume of the cone and that of the cylinder.

The sum of these volumes, is your answer.

Assume the following dimensions:

Cone

`r = 5\\` --- radius

`h = 7` --- height

Cylinder

`r = 5\\` --- radius

`h = 20` --- height

The volume of the cone is:

`Volume = (1)/(3) \pi r^2h`

`V_1= (1)/(3) \pi *5^2*7`

`V_1= (1)/(3) \pi *25*7`

`V_1= (175)/(3) \pi`

The volume of the cylinder is:

`Volume = \pi r^2h`

`V_2 = \pi * 5^2 * 20`

`V_2 = \pi * 25* 20`

`V_2 = 500\pi`

The total is:

`Volume = V_1 + V_2`

`Volume = (175\pi)/(3) + 500\pi`

Take LCM

`Volume = (175\pi+1500\pi)/(3)`

`Volume = (1675\pi)/(3)`