Question

if the radius of a right circular cylinder is halved find the ratio of the volume of the new cylinder form to its original one





प्लीज सॉल्व दिस क्वेश्चन ​

Answer 1

Given :-

• The figure taken is a right circular cylinder
• The ratio is made half of the original.

To find :-

The ratio of the new volume to the original volume.

Assuming the height to be h,

Let the original radius be 2r.

The new radius when made half = r

Volume of a cylinder = π × (radius)² × Height

By substituting the values,

The original volume = $\pi \times (2r)^{2} \times height$

=> $4\pi r^{2}h$

New volume after the radius is made half = $\pi \times r^{2} \times height$

=> $\pi r^{2}h$

Hence the ratio :

$\dfrac{\pi r^{2}h }{4\pi r^{2}h }$

Cancelling $\pi r^{2} h$ as it's common,

Ratio = 4 : 1

Some more formulas :-

Volume of cube = a³

Volume of cuboid = length × breadth × height

Volume of cone = $\pi \times (radius)^{2} \times \dfrac{height}{3}$