A vassel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vassel is 13 cm. Find the total surface area of the vassel. [use $\pi =\frac{22}{7}$] .

Academic Mathematics NCERT Class 10

Given: A vassel in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter.

The diameter of the hemispherical bowl $=14\ cm$ and the total height of the vassel $=13\ cm$

To do: To Find the total surface area of the vassel.

Solution:

Let the radius and height of cylinder be $r\ cm$ and $h\ cm$ respectively.

Diameter of the hemispherical bowl $=\ 14\ cm$

Radius of the hemispherical bowl = Radius of the cylinder$=\frac{14}{2}=7\ cm$

Total height of the vessel $=\ 13\ cm$

Height of the cylinder, $h=\ 13\ cm\ -\ 7\ cm\ =\ 6\ cm$

(Since, the vessel is hollow)

$Total\ surface\ area\ of\ the\ vessel=\ 2\ ( curved\ surface\ area\ of\ the\ cylinder\ +\ curved\ surface\ area\ of\ the\ hemisphere)$

$2( 2\pi rh+2\pi r^{2})$

$=4\pi r( h+r)$

$=4\times \frac{22}{7} \times 7( 7+6)$

$=88\times 13$

$=1144\ cm^{2}$

Therefore total surface area of the vassel is $1144\ cm^{2}$ .

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Updated on: 10-Oct-2022

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