Question

If a soild sphere with total surface area 48cm2 is bisected into two hemispheres, then find the
total surface area of any one of the hemisphere ?

Answer 1

Answer:

The total surface area of the hemisphere is 36 cm².

Step-by-step-explanation:

We have given that,

Total surface area of sphere = 48 cm²

The sphere is bisected into two hemispheres.

We have to find the total surface area of any one of the hemispheres.

Now, we know that,

$\displaystyle{\pink{\sf\:Total\:surface\:area\:of\:sphere\:=\:4\:\pi\:r^2}}$

$\displaystyle{\implies\sf\:48\:=\:4\:\times\:\dfrac{22}{7}\:\times\:r^2}$

$\displaystyle{\implies\sf\:r^2\:=\:\dfrac{48\:\times\:7}{4\:\times\:22}\:\quad\:\dots\:(\:1\:)}$

Now,

$\displaystyle{\blue{\sf\:Total\:surface\:area\:of\:hemisphere\:=\:3\:\pi\:r^2}}$

$\displaystyle{\implies\sf\:TSA_{Hemisphere}\:=\:3\:\times\:\dfrac{22}{7}\:\times\:\dfrac{48\:\times\:7}{4\:\times\:22}\:\quad\:\dots\:[\:From\:(\:1\:)\:]}$

$\displaystyle{\implies\sf\:TSA_{Hemisphere}\:=\:\dfrac{3\:\times\:\cancel{22}\:\times\:48\:\times\:\cancel{7}}{\cancel{7}\:\times\:4\:\times\:\cancel{22}}}$

$\displaystyle{\implies\sf\:TSA_{Hemisphere}\:=\:\dfrac{3\:\times\:\cancel{48}}{\cancel{4}}}$

$\displaystyle{\implies\sf\:TSA_{Hemisphere}\:=\:3\:\times\:12}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:TSA_{Hemisphere}\:=\:36\:cm^2}}}}$

∴ The total surface area of the hemisphere is 36 cm².

Answer 2

Answer:

Given :-

• A solid sphere with total surface area 48 cm² is bisected into two hemisphere.

To Find :-

• What is the total surface area of any one of the hemisphere.

Formula Used :-

$\clubsuit$ Total Surface Area of Sphere Formula :

$\longmapsto \sf\boxed{\bold{\pink{T.S.A\: of\: Sphere =\: 4{\pi}r^2}}}$

$\clubsuit$ Total Surface Area of Hemisphere Formula :

$\longmapsto \sf\boxed{\bold{\pink{T.S.A\: Of\: Hemisphere =\: 3{\pi}r^2}}}$

where,

• T.S.A = Total Surface Area
• r = Radius

Solution :-

First, we have to find the radius :

Given :

$\bigstar$ Total Surface Area = 48 cm²

According to the question by using the formula we get,

$\implies \sf 4 \times \dfrac{22}{7} \times r^2 =\: 48$

$\implies \sf r^2 =\: \dfrac{48 \times 7}{4 \times 22}$

$\implies \sf \bold{\green{r^2 =\: \dfrac{336}{88}}}$

Now, we have to find the total surface area of hemisphere :

Given :

$\bigstar \: \: \sf r^2 =\: \dfrac{336}{88}$

According to the question by using the formula we get,

$\longrightarrow \sf T.S.A\: of\: Hemisphere =\: 3 \times \dfrac{22}{7} \times \dfrac{336}{88}$

$\longrightarrow \sf T.S.A\: of\: Hemisphere =\: 3 \times \dfrac{\cancel{7392}}{\cancel{616}}$

$\longrightarrow \sf T.S.A\: of\: Hemisphere =\: 3 \times \dfrac{12}{1}$

$\longrightarrow \sf T.S.A\: of\: Hemisphere =\: 3 \times 12$

$\longrightarrow \sf\bold{\red{T.S.A\: of\: Hemisphere=\: 36\: cm^2}}$

$\therefore$ The total surface area or TSA of hemisphere is 36 cm².