The radius of a sphere is 3 cm. The radius of the base of a cone is also 3 cm.
The volume of the sphere is 3 times the volume of the cone.
Work out the curved surface area of the cone, giving your answer as a multiple of pi.
Thanks.
Hello GAdamsThe volume of a sphere is $\displaystyle \frac{4}{3}\pi r^3$, and the volume of a cone is $\displaystyle \frac{1}{3}\pi r^2h$. So:
$\displaystyle \frac{4}{3}\pi r^3 = 3\times \frac{1}{3}\pi r^2h = \pi r^2h$
$\displaystyle \Rightarrow h = \frac{4}{3}r = 4$ cm.
Can you finish it now?
Grandad
Let s denote the slanted height, r the radius of the base circle and h the height of the cone. Then the curved surface of a cone is a sector of a circle with radius s. The area of the curved surface, the area of the complete circle, the circumference of the base circle = arc of the sector and the circumference of the complete circle are directly proportional:
$\displaystyle \dfrac{a_{cs}}{\pi s^2} = \dfrac{2\pi r}{2\pi s}~\implies~a_{cs} = \dfrac{2\pi r}{2\pi s} \cdot \pi s^2 = \boxed{\pi r s}$
Hello GAdams
earboth has given you the formula for the curved surface area of a cone. You now need to work out the value of $\displaystyle s$, which you can do using Pythagoras' Theorem. (It's the easiest right-angled triangle of all!)
Then plug the values of $\displaystyle r$ and $\displaystyle s$ into this formula, and you're there.
Grandad