Question

Find the lateral surface area and the total surface area of a solid cylinder of height 14 cm ,If its volume is 686 pae cm³.​

Answer 1

Given :-

• Height of the cylinder is 14 cm

• Volume of the cylinder is 686 cm³

To Find :-

• Lateral and Total surface area of that Cuboid.

Solution :-

❍  To calculate the lateral and total surface area of this cylinder we must know that ::

• Volume of a cylinder = πr²h

• Lateral surface area of a cylinder = 2πrh

• Total surface area of cylinder = 2πr( h + r )

Where,

☀️ r denotes radius

☀️ π denotes 22/7

☀️ h denotes height

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Finding the radius :-

• As we are given the volume of the cylinder we can find the radius by putting the values.

⇝ 686 cm³ = 22/7 × r² × 14

⇝ 686 cm³ = 22 × r² × 2

⇝ 686 cm³ = 44r²

⇝ r² = 686/44

⇝ r² = 15.59

⇝ r  = √15.59

⇝ r = 3.94

Finding the Lateral surface area :-

⇝ 2 × 22/7 × 3.94 × 14

⇝ 2 × 22 × 3.94 × 2

⇝ 346.72 cm²

Finding the Total surface area :-

⇝ 2 × 22/7 × 3.94 × ( 3.94 + 14 )

⇝ 2 × 22/7 × 3.94 × 17.94

⇝ 444.29 cm²

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• Henceforth, Lateral surface area ( LSA ) is 346.72 cm² and Total surface area ( TSA ) is 444.29 cm²