Question

A solid cylinder of height 9m has its curved surface area equal to one third of the total surface area. What is the radius of the base?

Answer 1

GIVEN:

• Height of the cylinder = 9m
• Curved surface area equal to one third of the total surface area

TO FIND:

• What is the radius of its base ?

SOLUTION:

Let the radius of its base be 'r' m

We have given that, the curved surface area equal to one third of the total surface area.

We know that the formula for finding the C.S.A. of cylinder is:-

$\large{\boxed{\bf{\star \: C.S.A. = 2 \pi r h \: \star}}}$

We know that the formula for finding the T.S.A. of cylinder is:-

$\large{\boxed{\bf{\star \: T.S.A. = 2 \pi r (h + r) \: \star}}}$

According to question:-

$\large{\bf{\star \: 2 \pi r h = \dfrac{1}{3} 2 \pi r (h + r) \: \star}}$

On putting the given values in the formula, we get

$\rm{\hookrightarrow \cancel{2 \pi r} \times h = \dfrac{1}{3} \cancel{2 \pi r} (h + r) \: }$

$\rm{\hookrightarrow h = \dfrac{1}{3} \times h + r }$

$\rm{\hookrightarrow 9 = \dfrac{1}{3} ( 9 + r) }$

$\rm{\hookrightarrow 9 \times 3 = 9 + r }$

$\rm{\hookrightarrow 27 = 9+r }$

$\rm{\hookrightarrow 27 - 9 = r }$

$\bf{\hookrightarrow 18 \: m = r }$

❝ Hence, the radius of the base of the cone is 18 m ❞

______________________

Answer 2

Given that ,

• Height of cylinder (h) = 9 m
• CSA of cylinder =TSA of cylinder/3

According to the question ,

$\sf \Rightarrow 2\pi rh = \frac{ 2\pi {r}^{2} + 2\pi rh}{3} \\ \\ \sf \Rightarrow 6\pi rh = 2\pi r(r + h) \\ \\ \sf \Rightarrow 3h = r + h \\ \\ \sf \Rightarrow 2h = r$

Put the value of h = 9 , we get

$\sf \Rightarrow r = 2 \times 9 \\ \\ \sf \Rightarrow r = 18 \: \: m$

$\sf \therefore \underline{The \: radius \: of \: base \: of \: cylinder \: is \: 18 \: m}$