A toy is in the form of a cone of radius 3.5 cm

Question:

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.

Solution:

We have to find the total surface area of a toy which is a cone surmounted on a hemisphere.

Radius of hemisphere and the base of the cone $(r)=3.5 \mathrm{~cm}$

Height of the cone,

h = 15.5 − 3.5 = 12 cm

slant height $(l)=\sqrt{\mathrm{h}^{2}+\mathrm{r}^{2}}$

$=\sqrt{12^{2}+3.5^{2}}$

$=\sqrt{156.25}$

$=12.5 \mathrm{~cm}$

So, total surface area of toy,

$S=\pi r l+2 \pi r^{2}$

$=\pi r(l+2 r)$

$=\frac{22}{7} \times 3.5(12.5+2 \times 3.5)$

$=214.5 \mathrm{~cm}^{2}$

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