Math Is Fun Forum

unique

Member

Registered: 2006-10-04

Posts: 419

Help

---

Desi
Raat Key Rani !

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help

I'm assuming the text is meant to say

This figure is the base of a cone that is 8 inches tall.
What is the volume of the cone? Dimensions are in inches.

It's a curious property of cones that no matter how irregularly shaped its base is, its volume can always be worked out by (basearea x height)/3.

So if we can work out the area of that base, then the rest is easy.
The base is composed of a right-angled triangle and a sector of a circle.

Triangle: (8*12)/2 = 48.
Sector: π*8² * (50/360) = 80π/9.

Therefore, the total area of the base is 48 + 80π/9, which is ~ 75.9 square inches.

From here, we just need to multiply by the height and divide by 3, which gives a final area of:
(8/3)(48 + 80π/9) cubic inches if you're being exact, or ~202 cubic inches if you're approximating.

---

Why did the vector cross the road?
It wanted to be normal.