Question

The volume of a hemisphere is 2425.5cm3

. Find its curved surface area.​

Answer 1

Answer:

693 sqcm is the answer of the given question

Answer 2

$\: \bigstar\large\underline\green{\underline\frak{\underline{Given}} } :$

• The volume of a hemisphere = 2425.5 cm³

$\: \bigstar\large\underline\red{\underline\frak{\underline{to \: find}} } :$

• Find curved surface area of hemisphere?

$\: \bigstar\large\underline\green{\underline\frak{\underline{formula \: used}} } :$

• $\red{ \sf \:volume \: of \: hemisphere = \: \frac{2}{3} \pi {r}^{3}}$
• $\sf \purple{curved \: surface \: area \: of \: hemisphere \: = 2 {\pi r }^{2} }$

$\: \bigstar\large\underline\green{\underline\frak{\underline{solution}} } :$

We know that,

Volume of hemisphere = $\frac{2}{3} \pi {r}^{3}$

$\qquad \sf \longmapsto \: 2425.5 = \frac{2}{3} \pi {r}^{3 } \\ \\ \sf \longmapsto2425.5 = \frac{2}{3} \times \frac{22}{7} \times {r}^{3} \\ \\ \sf \longmapsto \: {r}^{3} = \frac{(2425.5)3 \times 7}{22 \times 2} \\ \\ \sf \longmapsto \: {r}^{3} = \frac{2425.5 \times 21}{44} \\ \\ \sf \longmapsto {r}^{3} = \cancel \frac{50935.5}{44} \\ \\ \: \sf \longmapsto \: { r}^{3} = 1157.625 \\ \\ \sf \longmapsto \: r = \sqrt{1157.625} \\ \\ \orange{ \boxed{\sf \longmapsto \frak{ r = 10.5}}}$

Now, we find curved surface area of hemisphere,

We know that curved surface area of hemisphere = $2\pi {r}^{2}$

$\sf \longmapsto curved \: surface_{(hemisphere) }= 2\pi {r}^{2} \\ \\ \sf \longmapsto curved \: surface_{(hemisphere) }= 2 \times \frac{22}{7} \times {(10.5)}^{2} \\ \\ \sf \longmapsto curved \: surface_{(hemisphere) }= 2 \times \frac{22}{7} \times 10.5 \times 10.5 \\ \\ \sf \longmapsto curved \: surface_{(hemisphere) }= \frac{2 \times 22 \times 10.5 \times 10.5}{7} \\ \\ \sf \longmapsto curved \: surface_{(hemisphere) }= \frac{44 \times 10.5 \times 10.5}{7} \\ \\ \sf \longmapsto curved \: surface_{(hemisphere) }= \cancel\frac{4851}{7} \\ \\ \sf \boxed{ \purple {{\frak{\longmapsto curved \: surface_{(hemisphere) }= 693 \: sq \: cm}}}}$

Hence, curved surface area of of hemisphere = 693 cm²