Question

the height of a cylinder is 14 cm and curved surface area is 264 cm find the volume of cylinder is​

Answer 1

CORRECT QUESTION :-

• The height of a cylinder is 14 cm and curved surface area is 264cm². Find the volume of Cylinder.

GIVEN :-

• Height of Cylinder = 14cm
• C.S.A of Cylinder = 264cm²

TO FIND :-

• Volume of Cylinder.

TO KNOW :-

★ C.S.A of Cylinder = 2πrh

★ Volume of Cylinder = πr²h

SOLUTION :-

• We are given C.S.A of the Cylinder. We will find radius of the Cylinder by applying formula. After getting the value of radius , we can find Volume of Cylinder.

C.S.A of Cylinder = 2πrh

We have ,

• C.S.A of Cylinder = 264cm²
• h = 14cm
• π = 22/7

Putting values,

264 = 2 × (22/7) × r × 14

264 = 88r

r = 264/88

r = 3cm

Hence , radius of Cylinder is 3cm.

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Volume of Cylinder = πr²h

We have,

• h = 14cm
• r = 3cm
• π = (22/7)

Putting values,

Volume of Cylinder = (22/7) × 3² × 14

Volume of Cylinder = 22 × 9 × 2

Volume of Cylinder = 396cm³

Hence , Volume of the Cylinder is 396cm³.

MORE FORMULA :-

★ Volume of Cone = (1/3)πr²h

★Volume of Cuboid = l × b × h

★ Volume of Cube = edge³

★ Volume of Sphere = (4/3)πr³

★ Volume of Hemisphere = (2/3)πr³

★ C.S.A of Cone = 2πrl

★ C.S.A of Cuboid = 2(lh+bh)

★ C.S.A of Cube = 4×edge²

★ T.S.A/C.S.A of Sphere = 4πr²

★ T.S.A/C.S.A of Hemisphere = 3πr²

Answer 2

Given :

• Curved Surface Area of Cylinder is 264cm²
• Height of Cylinder is 14cm

To Find :

• Volume of Cylinder

Solution :

✰ As we know that, Curved Surface Area of Cylinder is given by 2πrh where r and h stands for Radius and Height respectively. We also know that Volume of Cylinder is given by πr²h . Now in this question Curved Surface Area of Cylinder and Height of Cylinder are given and we have to find the volume of the Cylinder. For finding the volume of cylinder we need Radius of Cylinder . So Firstly we will find the Radius of Cylinder by applying 2πrh then we will find the Volume of Cylinder.

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Let's Do It ..!!⠀

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⟹ Radius of Cylinder :

• C.S.A of Cylinder = 2πh
• 264 = 2 × 22/7 × radius × 14
• 264 / 2 = 22/7 × radius × 14
• 132 = 22/7 × radius × 14
• 132 = 22 × 2 × radius
• 132 = 44 × radius
• 132 / 44 = radius
• 3cm = radius

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⟹ Volume of Cylinder :

• Volume = πr²h
• Volume = 22/7 × (3)² × 14
• Volume = 22/7 × 3 × 3 × 14
• Volume = 22/7 × 9 × 14
• Volume = 22 × 9 × 2
• Volume = 22 × 18
• Volume = 396cm³

Thus Volume of Cylinder is 396cm³

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$\small\boxed{\begin{array}{cc}\large \red{\boxed{\blue{\sf\dag \: {\underline{Formulae \: Related \: to \: Cylinder :}}}}} \\ \\ \bigstar \: \sf Area\:of\:Base\:and\:top =\pi r^2 \\ \\\bigstar \: \sf Curved \: Surface \: Area =2 \pi rh \\ \\ \bigstar \: \sf Total \: Surface \: Area = 2 \pi r(h + r) \\ \\ \bigstar \: \sf Volume=\pi r^2h \end{array}}$