Question

If the height and the diameter of base of a right circular cone be doubled, how many times will increase its volume?

Answer 1

The Volume of the cone will increase EIGHT times.

1st case,
consider the
diameter=2x cm⇒ radius=x cm 
height= h cm
Volume of the 1st Cone=$\frac{1}{3} \pi r^{2} h$
Putting the value we get,
Volume of 1st cone= $\frac{1}{3} \pi x×h$

2nd case, (since it gets double)
Consider the
Diameter= 4x⇒ radius= 2x cm
height= 2h cm
Putting the value we get,
Volume of 2nd cone= $\frac{1}{3} \pi 4 x^{2} ×2h$

Now divide the volume of 2nd Cone by 1st cone,
the answer remains is 8.
Hence, the volume increases by 8 times.