Question

A cylinder has a diameter of 6 and a height of 10 what is the closest total surface area

Answer 1

Given :

✰ Diameter of cylinder = 6cm

✰ Height of cylinder = 10cm

To Find :

✰ Total surface Area

Solution :

✰ Firstly we will find the radius of the cylinder That is Diameter/2.We know that Total surface area of cylinder is 2πr (h + r), Where h is (Height) 10cm and r is (Radius). By using this formula we can easily find the Total surface area of cylinder.

• Diameter (d) = 6cm

• Radius (r) = 6/2 = 3cm

• Height (h)= 10cm

T.S.A of cylinder = 2πr (h + r)

→ 2 × 22/7 × 3 (10 + 3)

→ 2 × 22/7 × 3 × 13

→ 2 × 22/7 × 39

→ 245.05cm²

∴ T.S.A of cylinder is 245.05cm²

Answer 2

Given :

• Diameter of Cylinder = 6cm
• Height of Cylinder = 10cm

To Find :

• Total Surface Area of Cylinder

Solution :

✰ As we know that, Total Surface Area of Cylinder is given by 2πr (h + r) . Now in this question, Diameter of Cylinder along with the height of the Cylinder are given and we have to find the Total Surface Area of Cylinder. So firstly we will find the Radius of the Cylinder, after that we will substitute the given values in the formula.

⠀⠀⠀

⠀⠀⠀⟼⠀⠀⠀Diameter = 2 × Radius

⠀⠀⠀⟼⠀⠀⠀6 = 2 × Radius

⠀⠀⠀⟼⠀⠀⠀6/2 = Radius

⠀⠀⠀⟼⠀⠀⠀3cm = Radius

⠀⠀⠀

⠀

And,

⠀

⠀⠀⠀⟼⠀⠀⠀TSA = 2πr (h + r)

⠀⠀⠀⟼⠀⠀⠀TSA = 2 × 22/7 × 3 (10 + 3)

⠀⠀⠀⟼⠀⠀⠀TSA = 44 × 3/7 × (10 + 3)

⠀⠀⠀⟼⠀⠀⠀TSA = 132/7 × (10 + 3)

⠀⠀⠀⟼⠀⠀⠀TSA = 18.85 × (10 + 3)

⠀⠀⠀⟼⠀⠀⠀TSA = 18.85 × 13

⠀⠀⠀⟼⠀⠀⠀TSA = 245.05cm²

⠀

Thus Total Surface Area of Cylinder is 245.05cm²

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