Question

The total surface area of a cone whose radius is 2r and slant height is 3l is ______.​

Answer 1

Given

• Radius of a cone = 2r
• Slant height of a cone = 3l

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To find

• Total surface area of the cone.

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Solution

• We have radius and slant height of a cone.

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As we know

⠀

☆ TSA = πrl + πr²

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• Putting the values

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→ TSA = π(2r)(3l) + π(2r)²

→ TSA = 6πrl + 4πr²

→ TSA = 2πr(3l + 2r)

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Hence,

• The total surface area of the cone is 2πr(3l + 2r) square units.

Answer 2

⠀⠀⠀⠀⠀⠀⠀Provided Data

A cone :

$\implies$Radius of a cone given as 2r

$\implies$Slant height of a cone given as 3l

⠀

⠀⠀⠀⠀⠀ Need to calculate

$\implies$What's the total surface area of the cone.

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⠀⠀⠀⠀ Appropriate Answer

Here, we just simply substitute the respective values in the formula for Total surface area of cone.

Formulas related to cone :

Total Surface Area :-

⠀⠀⠀⠀⠀$:\implies \bf{TSA = \pi r(r + l)}$

Volume of a Cone :-

⠀⠀$\bf{\underline{V = \dfrac{1}{3}\pi r^{2}h}}$

Curved surface Area :-

⠀⠀⠀⠀⠀$:\implies \bf{CSA = \pi rl}$

Where ,

H is Height of cone

R is radius of cone

L is length of cone.

$\underline{\bf{For\: Total \: Surface \: Area :-}}$

Substituting the respective values :

⠀

$\implies$ TSA = { π * 2r * 3l } + π(2r)²

$\implies$ TSA = 6πrl + 4πr²

$\implies\bf{TSA = 2πr(3l + 2r)}$

$\boxed{\therefore \bf{Total\:Area\: =2πr(3l + 2r) }}$

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