Question

Two cylinders have their radii in the ratio of 3:4 and their heights in the ratio 2:3. The ratio of their curved surface area is

Answer 1

Explanation:

1st case :

Let the radius be 3x

Let the height be 2y

so, CSA = 2πrh

=2π×3x×2y

2nd case :

Let the radius be 4x

Let the height be 3y

so, CSA =2πrh

= 2π ×4x×3y

Now, Ratio of their CSA =2π×3x×2y : 2π×4x×3y

=1:2

Answer 2

GIVEN:

• Radii of two cylinders are in the ratio = 3:4
• Height of the two cylinders = 2:3

TO FIND:

• What is the ratio of their surface areas ?

SOLUTION:

Let x be the common in given ratios of radii

• Radius of one cylinder = 3x
• Radius of another cylinder = 4x

Let y be the common in given ratios of height

• Height of one cylinder = 2y
• Height of another cylinder = 3y

To find the CSA of first cylinder, we use the formula:-

⠀✬ ❰ CSA = 2πrh ❱ ✬

According to question:-

➵ CSA = 2 $\times$ $\sf{\dfrac{22}{7}}$ $\times$ 3x $\times$ 2y

➵ CSA = $\sf{\dfrac{44}{7}}$ $\times$ 3x $\times$ 2y

To find the CSA of second cylinder, we use the formula:-

⠀✬ ❰ CSA = 2πrh ❱ ✬

According to question:-

➵ CSA = 2 $\times$ $\sf{\dfrac{22}{7}}$ $\times$ 4x $\times$ 3y

➵ CSA = $\sf{\dfrac{44}{7}}$ $\times$ 4x $\times$ 3y

Ratio of the CSA of two cylinders is:-

➵ $\sf{ \cancel\dfrac{44}{7}}$ $\times$ 3x $\times$ 2y : $\sf{ \cancel\dfrac{44}{7}}$ $\times$ 4x $\times$ 3y

⠀⠀⠀❮ RATIO = 1 : 2 ❯

❝ Hence, the ratio of the CSA of two cylinders is 1 : 2 ❞

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