Question

The curved surface area of a right circular cylinder is 4400 cm2 .If the circumference of the base is 110 cm, find the height of the cylinder.​

Answer 1

Curved surface area (C.S.A) of right circular cylinder = 4400cm²

In curved surface area, we take every part of cylinder except the area of two circle i.e at the bottom and at the top of cylinder.

So, the formula for curved surface area

• 2πrh

Its means 2πr is the circumference of circle and h is the height of cylinder

We have given, circumference of the base i.e 110cm

NOTE : Check the measuring unit.

In question we have to find out the height of cylinder. Now, we have given things are :-

• C. S. A = 4400cm²
• Circumference of base = 110cm

Apply the formula and solve the question

→ 2πrh = 4400

°• Here, 2πr is the circumference of base, and as we know that the value of circumference is already given. So, just put it.

→ 110 × h = 4400

→ h = 4400/110

→ h = 40 cm

If you want to convert it into S.I unit, it'll be :

• 1m = 100cm

•°• Height of cylinder = 0.4m

Answer 2

Answer:

Given :-

• The curved surface area of a right circular cylinder is 4400 cm².
• The circumference of the base is 110 cm.

To Find :-

• What is the height of the cylinder.

Formula Used :-

$\clubsuit$ Circumference Of Circle Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Circumference_{(Circle)} =\: 2{\pi}r}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius

$\clubsuit$ Curved Surface Area or C.S.A Of Cylinder Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Curved\: Surface\: Area_{(Cylinder)} =\: 2{\pi}rh}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

First, we have to find the radius :

Given :

• Circumference = 110 cm

According to the question by using the formula we get,

$\implies \bf Circumference_{(Circle)} =\: 2{\pi}r$

$\implies \sf 110 =\: 2{\pi}r$

$\implies \sf 110 =\: 2 \times \dfrac{22}{7} \times r$

$\implies \sf 110 =\: \dfrac{2 \times 22}{7} \times r$

$\implies \sf 110 =\: \dfrac{44}{7} \times r$

$\implies \sf 110 \times \dfrac{7}{44} =\: r$

$\implies \sf \dfrac{110 \times 7}{44} =\: r$

$\implies \sf \dfrac{770}{44} =\: r$

$\implies \sf 17.5 =\: r$

$\implies \sf\bold{\purple{r =\: 17.5\: cm}}$

Hence, the radius is 17.5 cm .

Now, we have to find the height of the cylinder :

Given :

• Curved Surface Area = 4400 cm²
• Radius = 17.5 cm

According to the question by using the formula we get,

$\small \implies \bf Curved\: Surface\: Area_{(Cylinder)} =\: 2{\pi}rh$

$\implies \sf 4400 =\: 2 \times \dfrac{22}{7} \times 17.5 \times h$

$\implies \sf 4400 =\: \dfrac{2 \times 22 \times 17.5}{7} \times h$

$\implies \sf 4400 =\: \dfrac{770}{7} \times h$

$\implies \sf 4400 \times \dfrac{7}{770} \times h$

$\implies \sf \dfrac{4400 \times 7}{770} =\: h$

$\implies \sf \dfrac{3080\cancel{0}}{77\cancel{0}} =\: h$

$\implies \sf \dfrac{\cancel{3080}}{\cancel{77}} =\: h$

$\implies \sf \dfrac{40}{1} =\: h$

$\implies \sf 40 =\: h$

$\implies \sf\bold{\red{h =\: 40\: cm}}$

$\therefore$ The height of the cylinder is 40 cm .

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