French, asked by eqkiihybgcjxykxglc, 8 months ago

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

Answers

Answered by anneshapaul770
5

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

Answered by ButterFliee
8

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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