Question

A cone has a base radius of 5cm and a height of 12cm, calculate its total surface area. leave your answer in terms of pi

Answer 1

Given:

• Base radius of cone = 5cm

• Height = 12cm

To Find:-

• It's total surface area in terms of π.

Formula used:-

• ${\boxed{TSA\: of\:Cone=\pi r(l+r)}}$

• ${\boxed{Slant Height (l)=\sqrt{r^2+h^2}}}$

Solution:-

Firstly,

$:\implies\:Slant Height (l)=\sqrt{r^2+h^2}$

$:\implies\:l=\sqrt{5^2+12^2}$

$:\implies\:l=\sqrt{25+144}$

$:\implies\:l=\sqrt{169}$

$:\implies\:{\underline{l=13cm}}$

Now,

$:\implies\:TSA\: of\:Cone=\pi r(l+r)$

$:\implies\:TSA=\pi\times 5(13+5)$

$:\implies\:TSA=\pi \times5\times18$

$:\implies\:{\underline{\bold{TSA = 90\pi}}}$

Hence, Total Surface Area of Cone in terms of π is 90π cm².

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More Formulas for Cone:-

• Lateral Surface Area = πrl

• Volume = $\sf \dfrac{1}{3}\pi r^2h$

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