Question

A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a height of 15 feet. The roof has an inclination angle of 25 degrees

Answer 1

a. 14.19 feet

b. 2504.26 cubic foot.

Explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

(a) Determine the height of the cone to the nearest tenth of a foot.

(b) Determine the overall volume of the tower to the nearest cubic foot.

Please have a look at the attached photo.

My answer:

Given the information:

The cylinder has:

• diameter of 12 feet => the radius : 6 feet
• height of 15 feet

The cone has: an inclination angle of 25 degrees

(a) Determine the height of the cone to the nearest tenth of a foot.

Let h is the height of the cone

The distance from C to A is 6 feet and the measure of the angle CAB is 25 degrees. The triangle ABC is a right triangle.

=> sin(CAB) =
`(CA)/(h)`

<=> h =
`(CA)/(sin25)`

<=> h =
`(6)/(sin25)`

<=> h = 14.19 feet

(b) Determine the overall volume of the tower to the nearest cubic foot.

overall volume = volume of the cone + volume of the cylinder

We have:

• Volume of the cylinder = the height*the base area

= 15*
`r^(2)`*π

= 15*
`6^(2)`*π

= 1696.6 cubic foot.

• volume of the cone = 1/3*the height*the base area

= 1/3*14.19*
`6^(2)`*π

= 534.76 cubic foot.

=> overall volume = 534.76 + 1696.6 = 2504.26 cubic foot.

Hope it will find you well.