Question

4. The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio
of their volumes is (2 marks)(with full solution)
(a) 10:17
(b) 20:27
(C) 17:27
(d) 20:37​

Answer 1

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Let the radii be 2x and 3x,

let the height be 5y and 3y.

so, ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27,

ratio of CSA =rh/RH =2x×5y/3x×3y =10xy/9xy =10/9.

the value of x and y can be termed to be get highes value and therefore bring forth in taking radius calculation

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Answer 2

Answer :–

• (b) is the correct option.

Given :–

• Radii of two cylinders are in ratio of 2:3.
• Heights are in the ratio of 5:3.

To Find :–

• Ratio of both cylinder volumes.

Solution :–

Let,

• The radius of 1st cylinder be 2r.

• And the radius of 2nd cylinder be 3r.

• The height of 1st cylinder be 5h.

• And the height of 2nd cylinder be 3h.

We know that,

Volume of cylinder = $\large\red{\pi {r}^{2} h}$

➲ In 1st cylinder,

• r = 2r.
• h = 5h.

↣ $\pi {(2r)}^{2} (5h)$ –––––(1)

➲ In 2nd cylinder,

• r = 3r.
• h = 3h.

↣ $\pi {(3r)}^{2} (3h)$ –––––(2)

Now, we have to find the ratio of both cylinders.

So,

Ratio of their volumes = $\boxed{ \red{\dfrac{volume \: of \: 1st \: cylinder}{volume \: of \: 2nd \: cylinder} }}$

Put, Eq. (1) and Eq. (2),

↣ $\dfrac{ \cancel{ \pi} {(2r)}^{2} (5h)}{ \cancel{ \pi} {(3r)}^{2}(3h) }$

↣ $\dfrac{ {4 \cancel{r}}^{2} \times 5h}{ {9 \cancel{r}}^{2} \times 3h}$

↣ $\dfrac{4r \times 5h}{9r \times 3h}$

↣ $\dfrac{20rh}{27rh}$

↣ $20\ratio27$

Hence,

The ratio of both cylinder volumes are 20:27.

So, the option (b) is correct.