Question

find the volume and the total surface area of a solid cylinder whose radius is 7 cm and its height is 30 cm​

Answer 1

Given :

✰ Radius and cylinder = 7cm

✰ Height of cylinder = 30cm

To Find :

✰ Volume and Total surface area of cylinder

Solution :

✰ As in the question Radius and height of cylinder is given. Firstly we will find volume of cylinder by Using formula πr²h. Then Total surface area of cylinder 2πr(h + r). We will fill the value of radius and height We can easily find the volume and surface area of the cylinder.

Volume of cylinder = πr²h

Where,

• Radius (r) = 7cm

• Height (h) = 30cm

→ 22/7 × (7)² × 30

→ 22/ 7 × 49 × 30

→ 22 × 7 × 30

→ 4650cm³

T.S.A of cylinder = 2πr(h + r)

→ 2 × 22/7 × 7( 7 + 30)

→ 2 × 22 × 37

→ 44 × 37

→ 1628cm²

∴ Volume of cylinder is 4650cm³

∴ T.S.A of cylinder is 1628cm²

Answer 2

Given :

• Radius of Cylinder (r) = 7cm
• Height of Cylinder (h) = 30cm

To Find :

• Volume of Cylinder
• Total Surface Area of Cylinder

Solution :

✰ As we know that, Volume of Cylinder and Total Surface Area of Cylinder are given by πr²h and 2πr (h + r) respectively. Now in this question Radius and Height of the Cylinder are given, so simply we will put the given values in the formula to find the Volume of Cylinder and Total Surface Area of Cylinder (TSA).

⠀⠀⠀

⠀⠀⠀⟼⠀⠀⠀Volume = πr²h

⠀⠀⠀⟼⠀⠀⠀Volume = 22/7 × (7)² × 30

⠀⠀⠀⟼⠀⠀⠀Volume = 22/7 × 7 × 7 × 30

⠀⠀⠀⟼⠀⠀⠀Volume = 22 × 7 × 30

⠀⠀⠀⟼⠀⠀⠀Volume = 22 × 210

⠀⠀⠀⟼⠀⠀⠀Volume = 4620cm³

⠀

And,

⠀

⠀⠀⠀⟼⠀⠀⠀TSA = 2πr (h + r)

⠀⠀⠀⟼⠀⠀⠀TSA = 2 × 22/7 × 7 (30 + 7)

⠀⠀⠀⟼⠀⠀⠀TSA = 2 × 22 × (30 + 7)

⠀⠀⠀⟼⠀⠀⠀TSA = 2 × 22 × 37

⠀⠀⠀⟼⠀⠀⠀TSA = 44 × 37

⠀⠀⠀⟼⠀⠀⠀TSA = 1628cm²

⠀

Thus Volume of Cylinder and Total Surface Area of Cylinder are 4620cm² and 1628cm² respectively.

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