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.

Given: 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 tower is $15.5\ cm$.

To do: To find the total surface area of the toy.

Solution:

As given,

Radius of cone $=$radius of hemisphere$=3.5\ cm$      $( given)$

Height of toy$=15.5\ cm$                    $( given)$

Height of hemisphere $=3.5\ cm$

Height of cone $=15.5-3.5=12\ cm$

Slant height of cone$=\sqrt{h^2+r^2}$

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

$=\sqrt{144+12.25}$

$=\sqrt{156.25}$

$= 12.5\ cm$

Curved Surface Area of hemisphere$=2\times\frac{22}{7}\times(3.5)^2$

$=77\ cm^2$

Curved Surface Area of cone$=\frac{22}{7}\times3.5\times12.5$

$=137.5\ cm^2$

Total Surface Area of toy=Curved Surface Area of hemisphere + Curved Surface Area of cone

$=77+137.5$

$=214.5\ cm^2$

 

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Updated on: 10-Oct-2022

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