Question

5. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio
5:3. Calculate the ratio of their curved surface areas.
​

Answer 1

Given :

• The radius of two cylinders are in the ratio of 2 : 3.
• Their heights are in the ratio 5 : 3.

To find :

• The ratio of their curved surface areas =?

Formula Used :

• Curved surface area cylinder = 2πrh

Step-by-step explanation :

Let, radius of first cylinder = $\tt r_1$

and height of the first cylinder =$\tt h_1$

∴ Curved surface area of first cylinder,$\tt S_1 =2 \pi r_1h_1$

Let radius of second cylinder =$\tt r_2$

and height of second cylinder =$\tt h_2$

∴ Curved Surface area of second cylinder,$\tt S_2 = 2 \pi r_2 h_2$

According to the question,

$:\implies \tt \dfrac{S_1}{S_2} = \dfrac{2 \pi r_1h_1}{2 \pi r_2 h_2}$

$:\implies\tt \dfrac{S_1}{S_2} = \dfrac{r_1h_1}{r_2 h_2}$

$:\implies\tt \dfrac{S_1}{S_2} = \dfrac{2_1 5_1}{3_2 3_2}$

$:\implies\tt \dfrac{S_1}{S_2} = \dfrac{2 \times 5}{3 \times 3}$

$:\implies\tt \dfrac{S_1}{S_2} = \dfrac{{10}}{{9}}$

Therefore, The ratio of their curved surface area is, 10 : 9.

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}$

• The radii of two cylinders are in the ratio 2 : 3
• heights are in the ratio
• 5:3

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• the ratio of their curved surface areas.

$\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}$

Let,

• Radius of first cylinder = r
• Height of first cylinder = h

Then,

★ Surface area of first cylinder (S) = 2πrh

Again,

• Radius of second cylinder = r'
• Height of second cylinder = h'

Then,

★ Surface area of second cylinder (S') = 2πr'h'

Now, A/C to question,

(The radii of two cylinders are in the ratio 2 : 3)

➩ r/r' = 2/3 -----------(1)

Again,

(heights are in the ratio

5:3)

➩ h/h' = 5/3 ------------(2)

Now, Calculate ratio of there surface area

➩ ( Surface area of first cylinder)/(Surface area of second cylinder) = 2πrh/2πr'h'

➩ S/S' = rh/r'h'

Keep Value by equ(1) & equ(2)

➩ S/S' = 2/3 × 5/3

➩ S/S' = 10/9

Or,

➩ S : S' = 10 : 9

$\Large{\underline{\underline{\mathfrak{\bf{\red{Hence}}}}}}$

• Ratio of there surface area will be = 10 : 9

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