The ratio between the radius of the base and the height of a cylinder is 2:3. If the volume of the cylinder is 12936 cm3. Find the radius of the base of the cylinder.
Given,
Ratio of the base and the height of a cylinder is 2:3
So,
Let the radius of the base = r
And
The height of the cylinder = h
r : h = 2 : 3
That is,
r/h = 2/3
So,
h = 3r/2 – – – – – – – – – (i)
As,
Volume of the cylinder = 12936 cm3
⇒ πr2h=12936
⇒ 22/7 × r2 × 3r/2=12936 [Using (i)]
⇒ 33/7 × r3=12936
⇒ r3 = 12936 × 7/33
⇒ r3 = 2744
⇒ r = 3√2744
Therefore,
r = 14 cm
So,
The radius of the base of the cylinder is 14 cm.