Question

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{Question:}}}}}}}\end{gathered}$
● The ratio between the curved surface area and the total surface area of a cylinder is 1:2. Find the ratio between the height and the
radius of the cylinder..
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Answer 1

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given:

→ Ratio between curved surface area and total surface area of a cylinder is 1 : 2.

We have to find out the ratio between height and the radius of the cylinder.

Formula to be used –

• Curved Surface Area = 2πrh
• Total Surface Area = 2πr(r + h)

Where,

• r - Radius of the cylinder.
• h - Height of the cylinder.

So, according to the question,

$\tt \implies \dfrac{2\pi rh}{2\pi r(r + h)} = \dfrac{1}{2}$

$\tt \implies \dfrac{h}{(r + h)} = \dfrac{1}{2}$

On cross multiplying, we get,

$\tt \implies 2h = r + h$

$\tt \implies 2h - h = r$

$\tt \implies h = r$

★ So, the ratio of height to radius will be - 1 : 1

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• 1 : 1

Answer 2

$\bf{\green{\underline{\underline{\orange{Answer :-}}}}}$

Given:-

The radius of the base of a right circular cylinder is halved and the height is doubled.

To find:-

What is the ratio of the volume of the new cylinder to that of the original one.

Solution:-

Let the radius of the base of a right circular cylinder be 'r' units and it's height be 'h' units

Volume of a cylinder = πr^2h cubic units

V1 = πr^2h cubic units -----------(1)

• Now if the radius is halved then the radius of the new cylinder = r/2 units

If the height is doubled then the height of the new cylinder =2h units

Volume of the new cylinder =

• V2 = π(r/2)^2×(2h) cubic units

• =>V2 = π×(r^2/4)×2h

• =>V2 = π×r^2×2h/4

=>V2 = πr^2h/2 cubic units----------(2)

Ratio of the volume of new cylinder to the original cylinder = V2:V1

=>πr^2h/2 : πr^2h

=>(πr^2h/2)/(πr^2h)

=>(1/2):1

=>1:2

Ratio = 1:2

Answer:-

Ratio of the volume of new cylinder to the original cylinder = 1:2

Used formulae:-

Volume of a cylinder = πr^2h cubic units

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