# geometry

A right circular cone is made from of a radius of 5 cm, a central angle of 216 degrees, what is the volume of the cone in cubic cm?

1. 👍 0
2. 👎 0
3. 👁 146
1. The key here is that the circumference of the base of the cone is equal to the arc length of the original sector.
arc-length/10π = 216/360
arc-length = 6π

if radius of cone is r,
2πr = 6π
r = 3

by taking a cross-section of the cone, we get a right-angled triangle with hypotenuse of 5, height of h and base segment of 3
so h^2 + 3^2= 5^2
h = 4

vol of cone = (1/3)π(3^2)(4) = 12π cm^3

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Related Rates

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile

asked by Anonymous on March 1, 2017
2. ### Calculus

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to

asked by Mishaka on December 16, 2011
3. ### Maths

A sector of a circle of radius 7cm subtending an angle of 270 degree at centre of the circle is use to form a cone? (A)find the base radius of the cone. (B)calculate the area of the base of the cone.

asked by Victor on February 2, 2016
4. ### math

Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft,

asked by rolan on August 13, 2012
5. ### Mathematics

A sector of a circle of radius 8cm is bent to form a cone.find the radius of the cone and its vertical angle if the angle subtended at the centre by the sector is 280

asked by Anonymous on July 2, 2020
1. ### Math

A cone is constructed by cutting a sector from a circular sheet of metal with radius 20cm. The cut sheet is then folded up and welded. Find the radius and height of the cone with the maximum volume that can be formed in this way.

asked by Lee Meyer on November 10, 2012
2. ### Calculus

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile

asked by Robin on July 5, 2013
3. ### math

The lateral surface of cone A is unwrapped into a sector of central angle 6 radians and radius π. What is the radius of cone A?

asked by sara on January 29, 2020
4. ### geometry

11. Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced

asked by Sarah on April 15, 2010
5. ### Geometry

Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by

asked by Sarah on April 17, 2010
6. ### Math 214

How do you find the volume of a right circular cone with a hemisphere? The height of the cone is 8 cm and the radius in 4cm.

asked by Calli on April 17, 2011