Question

3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius.
The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer 1

Step-by-step explanation:

Total surface area of toy = Curved surface area of cone + surface area of hemisphere

Curved surface area of cone = πrl

Where r=3.5cm, Height =15.5−3.5=12cm

And hence, l=12.5cm (by using formula l

2

=h

2

+b

2

)

Therefore C.S.A. of cone =π×3.5×12.5

=137.5cm

2

Surface area of hemisphere =2πr

2

=2×π×(3.5)

2

=77cm

2

Hence T.S.A of toy =77+137.5=214.5cm

2

Answer 2

Given :

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• Height of the toy = 15.5 cm
• Radius of base of the conical part (r) = 3.5 cm

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To Find :

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• Total surface area of the toy

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Solution :

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• Height of the conical part (h) = 15.5 - 3.5 = 12 cm

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$\huge{Slant \: height \: (l) = \sf{\sqrt{r²+h²}} }$

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$\implies\sf{\sqrt{(3.5)²+12²}}$

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$\implies\sf{\sqrt{12.25+144}}$

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$\implies\sf{\sqrt{156.25}}$

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$\implies\sf{12.5\:cm}$

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• ∴ Total surface area of the toy

$= \sf{πrl+2πr²}$

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$\implies\sf{πr\:(l+2r)}$

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$\implies\sf{\cfrac{22}{7}×3.5\:(12.5+2×3.5)\:cm²}$

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$\implies\sf{11\:(12.5+7)\:cm²}$

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$\implies\sf{11×19.5\:cm²}$

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$\implies{\purple{\underline{\boxed{\frak{214.5\:cm²}}}}{\:\bigstar}}$

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Hence, the total surface area of the toy is 214.5 cm².