Thread: trigonometry/ circle results help

hello,

A sector of a circle with radius 5cm and an angle of π/3 subtended at the centre is a cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

answer: 25π/6 cm^2

Originally Posted by maay

hello,

A sector of a circle with radius 5cm and an angle of π/3 subtended at the centre is a cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

answer: 25π/6 cm^2

The surface area of the cone is the same as the area of the sector.

Since the angle is , and a full circle is , this means that you have

of the circle.


So



.

Hello maay

Originally Posted by maay

hello,

A sector of a circle with radius 5cm and an angle of π/3 subtended at the centre is a cardboard. It is then curved around to form a cone. Find its exact surface area and volume.

answer: 25π/6 cm^2

The formula for the curved surface area of a cone is:

where is the radius and the slant-height of the cone.

So if the radius of the original cardboard circle is cm, can you see that this means that when the cardboard is formed into a cone?

So you can now:

• Use the formula above to find , given that

• Use Pythagoras' Theorem to find , the vertical height of the cone.
  

• Use the formula to find the volume of the cone.

Can you complete it now?

Grandad