Question

The volume and the curved surface area of a cylinder are 1650 cm^3 and 660 cm^2
respectively. Find the radius and height of the cylinder.​

Answer 1

Answer:

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Answer 2

Given :

• Volume of cylinder = 1650 cm³
• Curved surface area of cylinder = 660 cm²

To Find :

• Radius and height of the cylinder

Formula used :

$Volume = \pi {r}^{2} h$

$Curved \: surface \: area = 2\pi rh$

Solution :

Case I,

As we know,

$Curved \:surface \: area = 660$

$2\pi rh = 660 \\ \pi rh = 330$

Case II,

$Volume = 1650$

$\pi {r}^{2} h = 1650 \\ r(\pi rh) = 1650$

Using Case I, we have

$r(330) = 1650 \\ r = \frac{1650}{330} = 5 \: cm$

On Putting the value of r in Case I we get,

$\pi rh = 330 \\ \frac{22}{7} \times 5 \times h = 330 \\ h = \frac{330 \times 7}{22 \times 5} \\ h = 21 \: cm$

Therefore, the radius of the cylinder is 5 cm and the height is 21 cm.