The radius of a right circular cylinder is doubled keeping the height same. The ratio between the volumes of the new cylinder and the original cylinder is?
Answers
Answer:
1:4
Step-by-step explanation:
Let the new radius be r'.
Now volume of cylinder with radius r = πr²h
And volume of cylinder with radius r' = π(2r)²h
=4πr²h
Ratio of the two cylinders v1/v2 =
πr²h/4πr²h
=1/4
= 1:4
Given,
The radius of a right circular cylinder is doubled keeping the height the same.
.To find,
The ratio between the volumes of the new cylinder and the original cylinder.
Solution,
The ratio between the volumes of the new cylinder and the original cylinder will be 1:4.
We can easily solve this problem by following the given steps.
We know that the formula to find the volume of the cylinder is given as follows:
Volume = πr²h where r is the radius and h is the height of the cylinder.
For the old cylinder, let's take the radius to be r and height to be h units.
The volume of the old cylinder = πr²h
V1 = πr²h
Now, in the new case, when the radius of a right circular cylinder is doubled keeping the height the same, let's take the new radius to be r1.
r1 = 2r
The volume of the new cylinder = π(r1)²h
V2 = π(2r)²h
V2 = 4πr²h
The ratio of the volume of the old cylinder and new cylinder = πr²h:4πr²h
The ratio of the volume of the old cylinder and new cylinder = 1:4
Hence, the ratio of the volume of the old cylinder and the new cylinder is 1:4.