Question

The radii of two cylinders are in the ratio 4 : 8 and their heights are in the ratio 7 : 3. The ratio of their curved surface area is

Answer 1

Answer:

The ratio of their C. S. A. is 7 : 6

Step-by-step explanation:

Given that,

Radii of two cylinders in ratio -

→ 4 : 8

Height ratio -

→ 7 : 3

Step 1 : Let's assume

Radii of $\sf C_1$ (first cylinder)

→ $4x$

And height as,

→ $7x$

Radii of $\sf C_2$(second cylinder)

→ $8x$

Height

→ $3x$

Step 2 : Calculate the C. S. A. of $\sf C_1$

Curved surface area of a cylinder = 2πrh

We have,

• r (radius) = $4x$
• h (height) = $7x$

So, C. S. A. is -

$\to 2 \times \pi \times 4x \times 7x$

$\to 56 \pi{x}^{2}$

Step 3 : Calculate the C. S. A. of $\sf C_2$

Where,

• r is $8x$
• h is $3x$

So,

$\to 2\pi rh$

$\to 2 \times \pi \times 8x \times 3x$

$\to {48x}^{2}$

Step 4 : Form in ratio

$\to \sf S_1 : S_2$

Here,

• $\sf S_1 \: and \: S_2$ are the C. S. A. of first and second cylinder respectively.

$\to {56\pi x}^{2} : {48\pi x}^{2}$

$\to \sf \dfrac{56}{48}$

$\to \sf \frac{7}{6}$

$\to \sf 7: 6 \: ans.$

$\therefore$ The ratio of their C. S. A. is 7 : 6

Answer 2

Given:-

• Ratio of radii = 4:8
• Ratio of heights = 7:3

To find:-

• Ratio of their Curved Surface Areas

Formula:-

$\underline{\boxed{\sf C.S.A = 2πrh}}$

Solution:-

• let us assume the radius of 1st cylinder as 4x and the other one as 8x
• let the height of the 1st cylinder be 7x and 2nd be 3x

Curved Surface area of 1st cylinder :-

:$\implies$ $\sf :2×π×4x×7x = 56πx²$

Curved Surface Area of 2nd cylinder :-

:$\implies$ $\sf 2×π×8x×3x=48πx²$

Now, ratio between the two = $\sf\dfrac{56πx²}{48πx²}$ = $\sf\dfrac{7}{6}$

hence, the required ratio is 7:6