Question

The ratio of CSA and TSA of a right circular cylinder is 1:2.Find the ratio b\w the height and the radius of the cylinder.​

Answer 1

r is radius ...

h is height

Answer 2

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

$\green{\therefore{\text{Height:Radius=1:1}}}$

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

$\green{ \underline \bold{Given : }} \\ \implies \text{Ratio \: of} \: \: \: \: \: \frac{CSA}{TSA} = \frac{1}{2} \\ \\ \red{ \underline \bold{To \: Find : }} \\ \implies \text{Ratio \: of} \: \: \: \: \frac{Height}{Radius} = ?$

• In the given question information given about ratio of CSA and TSA of a right circular cylinder that is 1:2 and we have to find the ratio of their height and radius.

• According to given question :

$\implies \frac{CSA}{TSA} = \frac{1}{2} \\ \\ \implies 2 \times CSA= TSA \\ \\ \implies 2 \times (2\pi rh) = 2\pi r(h + r) \\ \\ \implies 4 \pi rh = 2\pi r(h + r) \\ \\ \implies \frac{4\pi rh}{2\pi r} = h + r \\ \\ \implies 2h = h + r \\ \\ \implies 2h - h = r \\ \\ \implies h = r \\ \\ \green{\implies \frac{h}{r} = \frac{1}{1} } \\ \\ {\green{\therefore \text{ratio \: of \: Height \: and \:Radius = 1 : 1}}}$