Find the volume of a right circular cone formed by joining the edges of a sector of a circle of radius r cm where the sector angle is 90 degrees.

Question

Find the volume of a right circular cone formed by joining the edges of a sector of a circle of radius r cm where the sector angle is 90 degrees.

I am not able to visualize this whole scenario. How can we do this one? What will be the radius and what will be the height of the cone after joining the edges? I will be really thankful if someone can just help me out with its figure

Answer 1

If I read this right, this can be visualized as follows: (1) Draw a circle of radius r on a piece of paper; (2) Cut out the circle; (3) Cut the circle in half along a diameter; (4) Cut one of the half-circles in half along a radius; (5) Take one of the quarter-circles and roll it up, joining the two radius-edges. (6) You now have a cone - calculate its volume.

Answer 2

You can use the circumference of the circle to get the circumference of the base of the cone. This will give you the radius of the base of the cone. Additionally, you have the slant height from the original radius - from these two, you can get the height of the cone.