A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are $ 6 \mathrm{~cm} $ and $ 4 \mathrm{~cm} $, respectively. Determine the surface area of the toy. (Use $ \pi=3.14 $ )

Given:

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are \( 6 \mathrm{~cm} \) and \( 4 \mathrm{~cm} \) respectively. 

To do:

We have to find the surface area of the toy. 

Solution:

Diameter of the base of the toy $= 6\ cm$

This implies,

Radius of the base $r = \frac{6}{2}$

$= 3\ cm$
Height of the conical part $h = 4\ cm$

Therefore,

Slant height of the conical part $l=\sqrt{r^{2}+h^{2}}$

$=\sqrt{3^{2}+4^{2}}$

$=\sqrt{9+16}$

$=\sqrt{25}$

$=5 \mathrm{~cm}$

Total surface area of the toy $=$ Curved surface area of the conical part $+$ Surface area of the hemispherical part

$= \pi r l + 2 \pi r^2$

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

$= 3.14 \times 3 \times (5 + 2\times3)$

$= 3.14 \times 3 \times 11$

$= 3.14 \times 33$

$= 103.62\ cm^2$

The surface area of the toy is $103.62\ cm^2$.

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Updated on: 10-Oct-2022

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