Name: Conversion of Solids
Uploaded: 2019-07-19
Duration: 5 min 33 s
Description: What happens when a goldsmith heats a gold bar to create something? The gold bar's shape gets changed. But what about its volume? Does it change too? Find ou...

Question

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are

13 cm

and

5 cm

respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is

12 cm

.

Accepted Answer

Given,
The height and radius of the cylindrical part are $13 cm and 5 cm$ , respectively.
i.e. $h = 13 cm, r = 5 cm$

The radii of the hemispherical and conical parts are the same as that of the cylindrical part.
$C S A$ of cylinder $= 2 π r h$
$= 2 \times \frac{22}{7} \times 5 \times 13$
$= \frac{2860}{7} {cm}^{2}$

Radius of hemispherical part $= r = 5 cm$
$C S A$ of hemispherical part
$= 2 π r^{2}$
$= 2 \times \frac{22}{7} \times 5 \times 5$
$= \frac{1100}{7} {cm}^{2}$

Radius of cone $= r = 5 cm$
Height of conical part $= h = 12 cm$
Slant height of the cone
$= l = \sqrt{r^{2} + h^{2}}$
$= \sqrt{5^{2} + 12^{2}}$
$= \sqrt{25 + 144}$
$= \sqrt{169}$
$= 13 cm$
$C S A$ of conical part
$= π r l$
$= \frac{22}{7} \times 5 \times 13$
$= \frac{1430}{7} {cm}^{2}$
Surface area of toy
$= C S A$ of cylinder $+ C S A$ of hemispherical part $+ C S A$ of conical part
$= \frac{2860}{7} + \frac{1100}{7} + \frac{1430}{7}$
$= \frac{5390}{7}$
$= 770 {cm}^{2}$

Therefore, the total surface area of the toy is $770 {cm}^{2}$ .

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