Question

5 The ratio between the curved surface area and the total surface area of a right circular cylinder is 4:9. Find the ratio between the height and the radius of the cylinder.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Height\:Radius=4:5}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies ratio \: of \: C.S.A : T.S.A= 4 : 9 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Ratio \: of \:Height : Radius = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{C.S.A\: of \: cylinder}{T.S.A \: of \: cylinder} = \frac{4}{9} \\ \\ \tt: \implies \frac{2\pi rh}{2\pi r(h + r)} = \frac{4}{9} \\ \\ \tt: \implies \frac{h}{h + r} = \frac{4}{9} \\ \\ \tt: \implies 9h = 4h + 4r \\ \\ \tt: \implies 9h - 4h = 4r \\ \\ \tt: \implies 5h = 4r \\ \\ \tt: \implies \frac{h}{r} = \frac{4}{5} \\ \\ \green{ \tt: \implies h : r = 4 : 5} \\ \\ \green{\tt \therefore Ratio \: of \:Height \: and \: Radius \: is \: 4 : 5}$

Answer 2

QUESTION :

5 The ratio between the curved surface area and the total surface area of a right circular cylinder is 4:9. Find the ratio between the height and the radius of the cylinder.

SOLUTION :

$\begin{lgathered}\bold{As \: we \: know \: that} \\ \tt: \leadsto \frac{C.S.A\: of \: cylinder}{T.S.A \: of \: cylinder} = \dfrac{4}{9} \\ \\ \tt: \mapsto \dfrac{2\pi rh}{2\pi r(h + r)} = \frac{4}{9} \\ \\ \tt: \implies \frac{h}{h + r} = \frac{4}{9} \\ \\ \tt: \implies 9h = 4h + 4r \\ \\ \tt: \implies 9h - 4h = 4r \\ \\ \tt: \implies 5h = 4r \\ \\ \tt: \implies \frac{h}{r} = \frac{4}{5} \\ \\ \green{ \tt: \implies h : r = 4 : 5} \\ \\ \purple{\tt \therefore Ratio \: of \:Height \: and \: Radius \: is \: 4 : 5}\end{lgathered}$