Question

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 vassel.​

Answer 1

${\huge {\underline {\blue {\bf {Question}}}}}$

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 vassel.

${\huge {\underline {\blue {\bf {Answer}}}}}$

Given :-

• The diameter of the hemisphere is 14 cm.

• Total height of the vessel is 13 cm.

To find :-

• The inner surface area of the vessel.

We Know :-

➢Diameter of the hemisphere = 14 cm

➢Radius of the hemisphere will be ${\sf {\frac {14}{2}}}$

➢Height of the hemisphere = Radius of the hemisphere = 7 cm

➢So, the radius of the cylinder will be 7 cm

➢Height of the cylinder = Height of the vessel – Height of the hemisphere

➢Height of the cylinder = 13 - 7 = 6 cm

${\bf {\purple {➢Curved\: surface\: area\: of\: cylindrical\: portion\: = 2πrh}}}$

➢$\sf 2 \times \frac {22}{ \cancel 7} \times \cancel 7 \times 6$

➢$\sf 2 \times 22 \times 6$

${\sf {\green {\underline {\boxed {➢264 {cm}^{2}}}}}}$

${\bf {\purple {➢Curved\: surface\: area\: of\: hemispherical\: portion\: = {2πr}^{2}}}}$

➢$\sf 2 \times \frac {22}{ \cancel 7} \times \cancel 7 \times 7$

➢$\sf 2 \times 22 \times 7$

${\sf {\green {\underline {\boxed {➢308 {cm}^{2}}}}}}$

∴ The inner surface area of the vassel = C.S.A. of cylindrical portion + C.S.A. of hemispherical portion

➢308 + 264

${\green {\underline {\boxed {\sf {{➢572cm}^{2}}}}}}$

Identities used!!!

${\sf {\purple {↝Curved\: surface\: area\: of\: hemisphere= {2πr}^{2}}}}$

${\sf {\purple {↝Curved\: surface\: area\: of\: cylinder = 2πrh}}}$

More Identities...!!

${\sf {\red {↝Volume\: of\: cylinder = {πr}^{2}h}}}$

${\sf {\red {↝Total\: surface\: area\: of\: cylinder = 2πr(h+r) }}}$

${\sf {\red {↝Volume\: of\: hemisphere = {\frac {2}{3} {πr}^{3}}}}}$

${\sf {\red {↝Total\: surface\: area\: of\: hemisphere = 3π{r}^{2} }}}$

Answer 2

Answer:

$\huge\bold\green{♡Answer♡}$

Complete step-by-step answer: We have the diameter of the hemisphere = 14cm. Hence the radius of the hemisphere =142=7cm..

I hope it helps u ☺️❣❣✌️..