Two cylinders have equal volume.Their heights are in the ratio 1:2.Find ratio of their radii? (9 std maths)

1 Answer
Dec 21, 2017

Solve for one height value equaling a multiple of the other, then substitute it into the formula for a cylinder's volume and use algebra to obtain

r_1/r_2 = sqrt(2).

Explanation:

We have that the formula for a cylinder's volume is

V_("cylinder") = pi r^2 h

Where r is the radius and h is the height. The given height ratio is

h_1/h_2 = 1/2

Where h_1 represents the height of the first cylinder, and h_2 represents that of second cylinder. We could solve for

h_1 = (h_2)/2

or

h_2 = 2 h_1

both of which we can use, if we were to consider the ratio between their volumes being equal:

(pi (r_1)^2 h_1)/(pi (r_2)^2 h_2) = 1

We could multiply the volume of the second cylinder to both sides to get

pi (r_1)^2 h_1 = pi (r_2)^2 h_2

Now, let's see, what can we do? We can substitute h_2 = 2 h_1:

pi (r_1)^2 h_1 = pi (r_2)^2 2 h_1

It seems that pi and h_1 both cancel out:

(r_1)^2 = 2(r_2)^2

Let's divide by (r_2)^2:

((r_1)^2)/((r_2)^2) = 2

And take the square root:

r_1/r_2 = sqrt(2)

We have just solved for the ratio between the radii, sqrt(2).