Question

If radii of two circular cylinders are in the ratio 3:4 and their heights are in the ratio
6:5, find the ratio of their curved surfaces.​

Answer 1

Answer:

first r=3x

h=6y

second r=4x

h=5y

curved surface area of first cylinder : curved surface area of second cylinder

3x ,6y : 4x,5y

both x,y of cylinder cut with eachother

18 :20 answer

Answer 2

Ratio of CSA of both Cylinders is 9:10

Given:

• If radii of two circular cylinders are in the ratio 3:4 ,
• Their heights are in the ratio 6:5.

To find:

• Find the ratio of their curved surfaces.

Solution:

Formula to be used:

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

here,

r: radius of cylinder

h: height of cylinder

Step 1:

It is given that radii are in ratio 3:4.

Let the radius of first cylinder is $r_1$ and radius of second cylinder is $r_2$

As,

$\frac{r_1}{r_2} = \frac{3}{4}$

As, there is a common factor in ratio, let the common factor is x here.

So,

$\bf r_1 = 3x$

and

$\bf r_2 = 4x$

Step 2:

Let the height of first cylinder is $h_1$ and that of second cylinder is $h_2$

According to the concept discussed in step 1.

Let the common factor of ratio of heights is y.

So,

$\bf h_1 = 6y$

and

$\bf h_2 = 5y$

Step 3:

Find the ratio of curved surface areas.

Let the CSA of cylinder 1 is C1 and that of cylinder 2 is C2.

$\frac{C_1}{C_2} = \frac{2\pi3x \times 6y}{2\pi4x \times 5y}$

cancel the common factors in numerator and denominator.

Ratio of CSA are $\bf \red{\frac{C_1}{C_2} = \frac{9}{10} }$

Thus,

Ratio of CSA of both Cylinders is 9:10

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