A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face.
Question:

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

 

Solution:

The radius of hemisphere as well as that of base of cone is r = 3.5 cm.
The height of toy = 15.5 cm.
The height of hemisphere, h = 3.5 cm and height of cone = 15.53.5 = 12 cm.

Using Pythagoras Theorem, slant height of cone is $l=\sqrt{(3.5)^{2}+(12)^{2}}=\sqrt{12.25+144}=\sqrt{156.25}=12.5 \mathrm{~cm}$.

Therefore, the Total surface area of toy = Curved surface of cone + Curved surface of hemisphere

$=\pi r l+2 \pi r^{2}=\frac{22}{7} \times 3.5 \times 12.5+2 \times \frac{22}{7} \times(3.5)^{2}$

$=\frac{275}{2}+77=\frac{275+154}{2}=\frac{429}{2}=214.5 \mathrm{~cm}^{2}$

 

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