Question

the radii of two of circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4. calculate the ratio of their curved surface areas and also the ratio of their volumes​

Answer 1

Answer:

surface area of cylinder 1

= 2pi×r×h+2pi×r^2

2×2X×22/7×5X+2×22/7×4X

2x×5x×4x×2×22/7×22/7

Answer 2

$\huge\sf\underline\red{Answer}$

Given :-

• Ratio of radii of two circular cylinders are 2:3

• Ratio of Heights of the Cylinder are 5:4

To Find :-

• Ratio of the Curved surface area of cylinder

• Ratio of the volume of cylinder

Solution :-

➣ Let the Radii of two circular cylinders be r and R

➣ Let the heights of cylinder be h and H

According to the question,

r : R = 2 : 3

$∴ \: \sf\dfrac{r}{ R} = \dfrac{2}{3}$

h : H = 5 : 4

$∴\sf \dfrac{h}{H} = \dfrac{5}{4}$

we know that,

Curved surface area of cylinders = 2πrh

Now,

$\sf Ratio \: of \: Surface \: area \: of \: cylinders = \dfrac{2\pi rh}{2\pi RH}$

By cancelling 2π on both we get ,

$\sf \: ⇒ \dfrac{r}{R} \times \dfrac{h}{H}$

By substituting values,

$\sf⇒ \dfrac{2}{3} \times \dfrac{5}{4}$

$\sf ⠀➱ \dfrac{5}{6}$

Hence, The Ratio of the Curved surface area of cylinders are 5 : 6

As we know that,

Volume of cylinder = πr²h

$\sf Ratio \: of \: the \: volume \: of \: cylinders = \dfrac{\pi {r}^{2}h }{\pi R²H}$

By Cancelling π on both we get,

$\sf \: ⇒ ( \dfrac{ {r} }{R} ) ^{2} \times \dfrac{h}{H}$

By substituting values,

$\sf⇒ ( \dfrac{2}{3} )^{2} \times \dfrac{5}{4}$

$⇒\dfrac{4}{9} \times \dfrac{5}{4}$

$\sf ⠀➱ \dfrac{5}{9}$

Hence, The Ratio of the volume of two cylinders are 5 : 9