Question

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

Answer 1

Let the radius and height of cylinder is $rcm$ and $hcm$ respectively.

Diameter of the hemisphere bowl $=14cm$

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

Total height of the vessel $=13cm$

Height of the cylinder, $h=$ Total height of the vessel $-$ Radius of the hemispherical bowl

$=13cm-7cm=6cm$

Total surface area of the vessel $=2$ (curved surface area of the cylinder + curved surface area of the hemisphere) (Twice because the vessel is hollow)

$=2(2\pi rh+2\pi r^2)=4\pi r(h+r)=4\times \frac{22}{7}\times 7\times (6+7)c{m}^2$
$=88\times 13$
$=1144c{m}^2$
Thus, the total surface area of the vessel is $1144c{m}^2.$