Question

Questions:-






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 vvassellss



:-Answer !!​

Answer 1

=> Radius=7cm

=> Height of the cylindrical portion13−7=6cm. 

Area of a Curved surface of cylindrical portion is,

=> 2πrh

=> 2×722×7×6

=> 264cm2

Area of a curved of hemispherical portion is

=> 2πr2

=> 2×722×7×7

=> 308cm2

∴ total surface area is = 308 + 264 = 572cm²

Answer 2

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

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.

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

$\underline{\boxed{\pink{\sf Given :-}}}$

• The diameter of the hemisphere is 14 cm.
• Total height of the vessel is 13 cm.

$\underline{\boxed{\pink{\sf To \: Find:-}}}$

• The inner surface area of the vessel.

$\underline{\boxed{\pink{We \: Know :-}}}$

➢Diameter of the hemisphere = 14 cm

➢Radius of the hemisphere will be 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

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

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

$➢\sf 2 \times 22 \times 6$

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

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

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

$➢\sf 2 \times 22 \times 7$

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

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

➢308 + 264

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

Identities used!!!

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

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

More Identities...!!

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

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

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

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