Math, asked by asmitshaw939, 19 days ago

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 and also the ratio of their volumes.

Answers

Answered by nilesh102

Given data : The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.

To find : Calculate the ratio of their curved surface areas and also the ratio of their volumes.

Solution : Let the radii of two circular cylinders be 2r and 3r and thier heights be 5h and 4h respectively.

Here, for first cylinder

For second cylinder

Now,

➜ Curved surface area of the first cylinder

= 2πrh

➜ Curved surface area of the first cylinder

= 2π * 2r * 5h

Here, CSA of 1st cylinder = 2π * 2r * 5h

and

➜ Curved surface area of the second cylinder

= 2πrh

➜ Curved surface area of the second cylinder

= 2π * 3r * 4h

Here, CSA of 2cd cylinder = 2π * 2r * 5h

Now,

➜ CSA of 1st cylinder : CSA of 2cd cylinder

= 2π * 2r * 5h/2π * 3r * 4h

➜ CSA of 1st cylinder : CSA of 2cd cylinder

= 2r * 5h/3r * 4h

➜ CSA of 1st cylinder : CSA of 2cd cylinder

= 10rh/12rh

➜ CSA of 1st cylinder : CSA of 2cd cylinder

= 10/12

➜ CSA of 1st cylinder : CSA of 2cd cylinder

= 5/6

➜ CSA of 1st cylinder : CSA of 2cd cylinder

= 5 : 6

Now,

➜ Volume of the first cylinder = πr²h

➜ Volume of the first cylinder = π * (2r)² * 5h

➜ Volume of the first cylinder = π * 4r² * 5h

Here, V of 1st cylinder = π * 4r² * 5h

and

➜ Volume of the second cylinder = πr²h

➜ Volume of the second cylinder = π * (3r)² * 4h

➜ Volume of the first cylinder = π * 9r² * 4h

Here, V of 2cd cylinder = π * 9r² * 4h

Now,