(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A right circular cone has height 6 cm and base radius 2. It is over-filled with ice cream,

in the usual way. Place the cone so its vertex is at the origin, and its axis lies along the

positive y–axis, and take the cross-section containing the x–axis. The top of this crosssection is a piece of the parabola y = 8 − x^{2}. The whole filled ice-cream cone is obtained

by rotating this cross-section about the y–axis.

What is the volume of the ice cream?

2. Relevant equations

y = 8 − x^{2}

3. The attempt at a solution

I have no idea how to work out this question,

but I think where you start off is by integrating y = 8 − x^{2}

so that ends up y = 8x - x^{3}/3

I just don't know how to get to the next step from here.

Many thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Circular cone volume through integration

**Physics Forums | Science Articles, Homework Help, Discussion**