The ratio between the curved surface area and the total surface area o

1.	The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.
Answer» Given, = \(\frac{curved\,surface\,area\,of\,cylinder}{total\,surface\,area\,of\,cylinder}\) = \(\frac{1}{2}\) Let radius of cylinder = r Let height of cylinder = h So, = \(\frac{2πrh}{2πr(h+r)}\) = \(\frac{1}{2}\) = \(\frac{h}{h+r}\) = \(\frac{1}{2}\) = 2h = h + r = 2h - h = r = h = r, height = radius

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.

Answer»

Given,

= \(\frac{curved\,surface\,area\,of\,cylinder}{total\,surface\,area\,of\,cylinder}\) = \(\frac{1}{2}\)

Let radius of cylinder = r

Let height of cylinder = h

So,

= \(\frac{2πrh}{2πr(h+r)}\) = \(\frac{1}{2}\)

= \(\frac{h}{h+r}\) = \(\frac{1}{2}\)

= 2h = h + r

= 2h - h = r

= h = r, height = radius