Question

a right Triangle having side 6cm, 8 CM, and 10 CM is revolve about the side of length 6cm. Find the volume .

Answer 1

cone will be formed whose height will be 6cm and radius will be 8cm.
use formula of volume of cone i.e. pi*r^2 *h/3 to find volume

Answer 2

Answer:

$128\pi cm^3$

Step-by-step explanation:

If the triangle is rotated about the 6cm side, it'll trace out a cone, of radius equal to 8cm, and height equal to 6cm. (since height stays stationary, and the farthest point from the axis remains at 8cm)

Note that the above bracketed explanation isn't quite enough in a rigorous manner, but you get the feel, don't you?

Now, the volume of a cone is:

$V = \frac{1}{3}\pi r^2h$

Substituting the values so deduced,

$V = \frac{1}{3}\pi (8)^2 6 cm^3$

Or, $V = 128\pi cm^3$