Question

the curved surface area and volume of a cylinder are 132m square and 99m square respectively . Find out the radius and height .

Answer 1

Given:

• The curved surface area of a cylinder = 132m sq.
• And the volume of the cylinder is 99m square.

To be found:

The height and the radius of the cylinder.

Some formula

$CSA\ of\ cylinder = \boxed{2\pi r h}\ unit\ sq.$

$\sf Volume\ of\ the\ cylinder = \boxed{\pi r^{2} h\ unit\ cube}$

[∵ In which 'r' is the 'radius' and 'h' is the 'height' of the cylinder ]

So,

$\implies 132 = 2 \times \frac{22}{7}\times r \times h$

$\implies 132 = \frac{44}{7}\times r \times h$

$\implies 132 \times \frac{7}{44}= r \times h$

$\implies 3 \times 7 = rh$

$\implies \boxed{rh = 21}$ ......(i)

Now,

The volume of the cylinder = $\pi r^{2} h\ unit cube$

$\implies 99 = \frac{22}{7} \times r \times \underline{ \bf r \times \bf h}$

Putting the value of eq(i), 'rh' = 21, we get,

$\implies 99 = \frac{22}{7} \times r \times \underline{\bf 21}$

$\implies 99 = 22 \times r \times 3$

$\implies 99 = 66 \times r$

$\implies \frac{99}{66} = r$

$\implies \boxed{1.5 m = r }$

Now,

From eq.(i)

rh = 21

⇒ 1.5 ×  h = 21

⇒ h = 21 ÷ 1.5

⇒ h = 14m

$\star$ Hence

The radius = 1.5m

And height = 14m

Answer 2

Answer :

C.S.A of cylinder = 132 m²

→ 2πrh = 132

→ 2 * 22/7 * r * h = 132

→ 44/7 * r * h = 132

→r * h = 3 * 7

→ r * h = 21 ....………(1)

___________________

Volume of cylinder = 99 m³

→ πr²h = 99

→ 22/7 * r * r * h = 99

★ From equation (1). [r* h = 21]

→ 22/7 * 21 * r = 99

→ 22 * 3 * r = 99

→ 66 * r = 99

→ r = 99/66

→ r = 3/2

→ r = 1.5 m

__________________

Now, Put value of r in equation (1).

→ 1.5 * h = 21

→ h = 21/1.5

→ h = 14 m