Question

23) Curved surface area of a cylinder is 4400cm square the cirumference of its base is 110 cm. Find the height of the cylinder
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Answer 1

$\huge\underline \mathfrak\orange{Answer}$

Let the radius and height of the given cylinder be r and h respectively.

 

Given :-

Circumference of base = 110 cm

$=> 2πr = 110cm$ .........................(1)

$=> 2 ×$ $\frac{22}{7}r = 100cm$

$=> r =$ $\frac{110 × 7}{44}cm$ = $\frac{35}{2}cm$

and C.S.A of cylinder = $4400 cm²$

$⇒ 2πrh = 4400 cm²$

Putting the value of 2πr from equation (1) we get

$110 h = 4400$

$h =$ $\frac{4400}{110}cm$ = $40cm$

 

∴ Volume of the cylinder = $πr²h$

= $\frac{22}{7}$×$\frac{(35)²}{(2)}$$× 40cm³$

= $\frac{22}{7}$×$\frac{35}{2}$×$\frac{35}{2}$$× 40cm³$

Hence height and volume of the given cylinder are 40 cm and 38500 cm³. 

$<font color="</strong><strong>orange</strong><strong>">$$<b >$$<marquee>$Hope it helps

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Answer 2

Given :-

• Curved surface area (C. S. A.) of Cylinder = 4400 cm²
• Circumference of its base = 110 cm

To FinD :-

• The height of the Cylinder

Solution :-

Let the height of the Cylinder is 'h' and the radius is 'r'

We know that :-

• Circumference = 2πr

So,

$\longrightarrow 2\pi r = 110$

We know that :-

• C. S. A of the Cylinder = 2πrh

$\longrightarrow 2\pi rh \: = 4400 \\ \\ \longrightarrow 110 \times h = 4400 \\ \\ \longrightarrow h = \frac{4400}{110} \\ \\ \longrightarrow h = \frac{440}{11} \\ \\ \longrightarrow h = 40$

Hence the height of the Cylinder is 40 cm