surface areas n volumes
Asked by | 8th Nov, 2008, 12:00: AM
The volume of a cone may be thought of as a special case of the volume
of a cylinder. The volume of a prism-like object is equal to its base
area times its height. That is true for any solid for which each cross
section is identical at any height. A box and a cylinder are examples.
This is known as Cavalerri's principal. That is where the Pi*r*r comes
into the problem. The base area of a cone and cylinder is a circle.
If the base on the top is reduced to a similar shape, but smaller
size, the volume decreases. It doesn't matter what shape the top and
bottom are, this is true for all of them. If we reduce the similar
shape at the top to a single point, we make a pyramid or cone. The
volume of this new figure is 1/3 the volume of the prism-like form.
We need calculus to prove this rigorously
Answered by | 8th Nov, 2008, 09:19: AM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number