Question

the radii of two right 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​

Answer 1

$\large\bf\underline{Given:-}$

• Ratio of radii of two circular cylinders = 2:3
• Ratio of height of circular cylinders = 5:4

$\large\bf\underline {To \: find:-}$

• Ratio of their curved surface areas.

$\huge\bf\underline{Solution:-}$

Let the radii of two circular cylinders be 2x and 3x.

Let the height of two circular cylinders be 5y and 4y.

Curved surface area of cylinder :-

$\underline{ \boxed{ \bf \:CSA = 2 \pi \: rh }}$

CSA of 1st cylinder having Radius 2x and height 5y.

$\rm \leadsto \: CSA = 2 \pi \: 2x \: 5y \\ \rm \leadsto \: CSA =20 \pi \: xy$

CSA of 2nd cylinder having Radius 3x and height 4y.

$\rm \leadsto \: CSA = 2 \pi \: 3x \: 4y \\ \rm \leadsto \: CSA =24 \pi \: xy$

Now, ratio of curved surface areas of both cylinders is :-

$\rm \mapsto \: \frac{CSA \: of \: 1st \: cylinder}{CSA \: of \: 2nd \: cylinder} \\ \\ \rm \mapsto \: \frac{20 \cancel{\pi \: xy}}{24 \cancel{\pi \: xy}} \\ \\ \rm \mapsto \: \cancel\dfrac{20}{24} \\ \\ \rm \mapsto \: \frac{5}{6}$

So, ratio of Curved surface areas of both cylinders is 5:6

Answer 2

Answer :

The ratio of their curved surface area is 5 : 6

$\rule{100}2$

Let the common factor in their ratios be ' p '

So,

• Radii of 1st cylinder = 2p
• Radi of second cylinder = 3p

Also,

• Height of 1st cylinder = 5h
• Height of 2nd cylinder = 4h

We know that,

→ C.S.A of cylinder = 2πrh

Now,

Ratio of 1st cylinder to 2nd cylinder :

$\sf = \dfrac{2\pi(2p)(5h)}{2\pi(3p)(4h)}$

$\sf = \dfrac{10p}{12p}$

$\sf = \dfrac{5}{6}$

Therefore,

Ratio of their C.S.A is 5:6.

$\rule{200}2$