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Question

An ice cream cone has radius of $$21$$ m and height of $$20$$ m. Find total surface area of the cone.


A
3297 m2
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B
9734 cm2
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C
3297 mm
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D
3297 m
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Solution

The correct option is A $$\displaystyle 3297{\  m }^{ 2 }$$
Given, radius $$r=21 m$$ and height $$h=20m$$.

Then, slant height is:
$$\displaystyle { s }^{ 2 }={ h }^{ 2 }+{ r }^{ 2 }$$
$$\implies$$ $$\displaystyle { s }^{ 2 }={ 20 }^{ 2 }+{ 21 }^{ 2 }$$
$$\implies$$ $$\displaystyle { s }^{ 2 }=400+441$$
$$\implies$$ $$\displaystyle s=\sqrt { 841 } $$
$$\implies$$ $$\displaystyle s=29$$ m.

Therefore, Total surface area of a cone $$\displaystyle =\pi rs+\pi { r }^{ 2 }$$
$$\displaystyle =3.14\times 21\times 29+3.14\times 21\times 21$$
$$\displaystyle =1912.26+1384.74$$
$$\displaystyle =3297{ m }^{ 2 }$$.

Hence, option $$A$$ is correct.

Mathematics

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