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:
$\displaystyle A = \pi r l$
where $\displaystyle r$ is the radius and $\displaystyle l$ the slant-height of the cone.
So if the radius of the original cardboard circle is $\displaystyle 5$ cm, can you see that this means that $\displaystyle l = 5$ when the cardboard is formed into a cone?
So you can now:
- Use the formula above to find $\displaystyle r$, given that $\displaystyle A = \frac{25\pi}{6}$
- Use Pythagoras' Theorem to find $\displaystyle h$, the vertical height of the cone.
- Use the formula $\displaystyle V = \tfrac13\pi r^2h$ to find the volume of the cone.
Can you complete it now?
Grandad