Question

The ratio of radii of two right circular cylinders are 6: 7 and their heights are in the ratio 5 : 9. the ratio of their respective curved surface area is

Answer 1

Hello friend, here is your answer.

Let r:R = 6:7 and h:H = 5:9.
Curved Surface Area of lst cylinder/ Curved Surface Area of second cylinder
= 2πrh/2πRH
= 2π×6×5/2π×7×9
= 6×5/7×9
= 30/63
= 10/21
= 10:21

Hope it helps you.
With regards@
Tanisha

Answer 2

Ratio of CSA of both cylinders are 10:21.

Given:

• The ratio of radii of two right circular cylinders are 6: 7, and
• Their heights are in the ratio 5 : 9.

To find:

• Find the ratio of their respective curved surface area.

Solution:

Formula to be used:

Curved surface area of cylinder: $\bf CSA = 2\pi \: rh$

Step 1:

Let the radius and height of first cylinder are $r_1$ and $h_1$ respectively.

and radius and height of second cylinder are $r_2$ and $h_2$ respectively.

ATQ

$\frac{r_1}{r_2} = \frac{6}{7}$

and

$\frac{h_1}{h_2} = \frac{5}{9}$

Step 2:

Find the ratio of CSA of both cylinders.

$\frac{CSA_1}{CSA_2} = \frac{2\pi \: r_1h_1}{2\pi \: r_2h_2}$

or

$\frac{CSA_1}{CSA_2} = \frac{r_1}{r_2} \times \frac{h_1}{h_2}$

or

$\frac{CSA_1}{CSA_2} = \frac{6}{7} \times \frac{5}{9}$

or

$\bf \frac{CSA_1}{CSA_2} = \frac{10}{21}$

Thus,

Ratio of CSA of both cylinders are 10:21.

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