Question

2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The
diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the
inner surface area of the vessel.​

Answer 1

Solution :-

Hemisphere :-

Diameter = 14 cm

Radius = 14/2 = 7 cm

Curved surface area of hemisphere $= \sf 2\pi r^2$

$\longrightarrow \sf 2 \times \dfrac{22}{7} \times 7^2 \\\\\longrightarrow 2 \times \dfrac{22}{7} \times 7 \times 7 \\\\\longrightarrow 2 \times 22 \times 7 \\\\\longrightarrow 308 \ cm^2$

Cylinder :-

Height of the cylinder = Total height - Radius of hemisphere

                                     = 13 - 7

                                     = 6 cm

Radius of cylinder = Radius of hemisphere

                              = 7 cm

Curved surface area of cylinder = $\sf 2\pi r h$

$\longrightarrow \sf 2 \times \dfrac{22}{7} \times 7 \times 6 \\\\\longrightarrow 2 \times 22 \times 6 \\\\\longrightarrow 264 \ cm^2$

According to the question :-

Inner surface area of the vessel = Curved surface area of hemisphere + Curved surface area of cylinder

$\longrightarrow \sf 308 + 264 \\\\\longrightarrow 572 \ cm^2$

Inner surface area of the vessel = 572 cm²

Answer 2

$\underline{\sf{\red{Given:-}}}$

• $\sf\ Radius=7cm$
• $\sf\ Height\: of\: the\: cylindrical\: portion\:13−7=6cm.$

$\underline{\sf{\red{To\: Find:-}}}$

• $\sf\ Inner\: surface\:area\:of\:the\: vessel$

$\sf\ Area\: of \:a\: Curved \:surface\: of\: cylindrical\: portion\: is,$

$\dashrightarrow\: \sf\ 2πrh$

$\dashrightarrow\: \sf\ 2× \dfrac{22}{7} ×7×6$

$\dashrightarrow\: \sf\ 264cm^2$

$\sf\ Area\: of \:a \:curved \:of \:hemispherical\: portion\: is$

$\dashrightarrow\: \sf\ 2πr^2$

$\dashrightarrow\: \sf\ 2× \dfrac{22}{7} ×7×7$

$\dashrightarrow\: \sf\ 308cm^2$

∴ $\sf\ total\: surface\: area\: is$

$\dashrightarrow\: \sf\ 308+264$

$\dashrightarrow\: \sf\ 572cm^2$

Hence,

• $\sf\ Total \:surface \:area = 572cm^2$