Thread: Ratio is given, how can I find the slant height? Thank you for the help c:

So this is the question (it's a volume question, and I'm pretty sure I can figure out the second part of finding the volume but finding the slant height seems very difficult here!) And it would also be very very helpful if you guys can point out as to how to get the answer.
Q: The ratio of the slant height and perpendicular height of a cone is 5:4. The diameter of the base is 12cm. Find the slant height of the cone.

All help greatly appreciated

This is really not a question about volume at all, but rather simple ratios and triangles. Imagine slicing the cone vertically so you get an isoceles triangle, where the "slant height" is the length of the two equal sides. Now imagine curtting that triangle in two, so that you have two right angle triangles, with the slant height being the hypotenuse. You are given the ratio of hypotenuse to height, so you can use Pythagoras to find the ratio of the hypotenuse to the radius of the cone's base. From that simply multiply that ratio by the radius of the base to get the hypotenuse, which is the same as the slant height of the cone.

Thank you for your help c: