Question

Find the total surface area of a cone,if its slant height is 20 m and dimeter of its base is 23 m

Answer 1

Given :

⠀⌬ Slant height of a cone = 20 m

⠀⌬ Diameter of the base of the cone = 23 m

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To find :

⠀⠀⠀⌬ The total surface area of the cone.

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Formula to be used :

$\bf\dag$ $\sf\color{green}{Total~surface~area~of~a~cone~=~πr(r+l)}$

where -

• π = 22/7
• r = radius of the cone
• l = slant height of the cone

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$\bf\dag$ $\sf\color{green}{Radius~=~\frac{diameter}{2}}$

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Solution :

We need the radius of the cone for calculating it's total surface area . Therefore calculating the radius of the cone at first -

$\sf\:Radius~=~\frac{diameter}{2}$

Substituting the given values

$\sf\implies\:Radius~=~\frac{23}{2}$

$\bf\implies\:Radius~=~11.5~m$

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Now calculating the total surface area of the cone -

$\sf\:Total~surface~area~of~a~cone~=~πr(r+l)$

Substituting the given values

$\sf\implies\:Total~surface~area~of~a~cone~=~\frac{22}{7}(11.5+20)$

$\sf\implies\:Total~surface~area~of~a~cone~=~3.14(11.5+20)$

$\sf\implies\:Total~surface~area~of~a~cone~=~3.14(31.5)$

$\sf\implies\:Total~surface~area~of~a~cone~=~3.14 \times 31.5$

$\sf\implies\:Total~surface~area~of~a~cone~=~\frac{314}{100} \times \frac{315}{10}$

$\sf\implies\:Total~surface~area~of~a~cone~=~\frac{314}{100} \times \frac{315}{10}$

$\sf\implies\:Total~surface~area~of~a~cone~=~\frac{98910}{1000}$

$\sf\implies\:Total~surface~area~of~a~cone~=~\frac{9891\cancel{0}}{100\cancel{0}}$

$\sf\implies\:Total~surface~area~of~a~cone~=~\frac{9891}{100}$

$\small{\underline{\boxed{\mathrm{\implies~Total~surface~area~=~98.91~sq~m}}}}$ $\sf\color{red}{⋆}$

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$\bf\therefore\:The~total~surface~area~of~cone~is~98.91~sq~m$

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Some more formula :

• Slant height = √r² + h²
• Volume = πr²h/3
• Lateral surface area = πr√h² + r²
• Base area = πr²

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