A toy is in the form of a cone of radius $ 3.5 \mathrm{~cm} $ mounted on a hemisphere of same radius. The total height of the toy is $ 15.5 \mathrm{~cm} $. Find the total surface area of the toy.
Given:
A toy is in the form of a cone of radius \( 3.5 \mathrm{~cm} \) mounted on a hemisphere of same radius.
The total height of the toy is \( 15.5 \mathrm{~cm} \).
To do:
We have to find the total surface area of the toy.
Solution:
Radius of the cone $r = 3.5\ cm$
Total height of the toy $H= 15.5\ cm$
Height of the conical part $h = 15.5 - 3.5$
$= 12\ cm$
This implies,
Slant height of the cone $l=\sqrt{r^{2}+h^{2}}$
$=\sqrt{(3.5)^{2}+(12)^{2}}$
$=\sqrt{12.25+144}$
$=\sqrt{156.25}$
$=12.5 \mathrm{~cm}$
Therefore,
Total surface area of the toy $=$ Curved surface area of the conical part $+$ Curved surface area of the hemispherical part
$=\pi r l+2 \pi r^{2}$
$=\pi r(l+2 r)$
$=\frac{22}{7} \times 3.5(12.5+2 \times 3.5)$
$=\frac{22}{7} \times \frac{7}{2}(12.5+7)$
$=11(19.5)$
$=214.5 \mathrm{~cm}^{2}$
The total surface area of the toy is $214.5\ cm^2$.
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