Question

3. Find the volume of the hemisphere whose total surface area is 2772 m^2​

Answer 1

Answer:

The volume of the hemisphere is 19404 cm3.

Answer 2

Answer:

The volume of hemisphere is 15853.2 m³.

Step-by-step explanation:

Firstly, finding the radius of hemisphere by substituting the values in the formula :

$\quad{\longrightarrow{\pmb{\sf{Tsa = 3\pi{r}^{2}}}}}$

• Tsa = Total surface area
• π = 22/7
• r = radius

$\quad{\longrightarrow{\sf{Tsa = 3\pi{r}^{2}}}}$

$\quad{\longrightarrow{\sf{2772 = 3 \times \dfrac{22}{7} \times {r}^{2}}}}$

$\quad{\longrightarrow{\sf{2772 =\dfrac{3 \times 22}{7} \times {r}^{2}}}}$

$\quad{\longrightarrow{\sf{2772 =\dfrac{66}{7} \times {r}^{2}}}}$

$\quad{\longrightarrow{\sf{{r}^{2} = 2772 \times \dfrac{7}{66} }}}$

$\quad{\longrightarrow{\sf{{r}^{2} = \cancel{2772}\times \dfrac{7}{\cancel{66}}}}}$

$\quad{\longrightarrow{\sf{{r}^{2} = 42 \times 7}}}$

$\quad{\longrightarrow{\sf{{r}^{2} = 294}}}$

$\quad{\longrightarrow{\sf{r = \sqrt{294}}}}$

$\quad{\longrightarrow{\sf{\underline{\underline{\red{r \approx 17.15 \: m}}}}}}$

Hence, the radius of hemisphere is 17.15 m.

———————————————————————

Now, finding the volume of hemisphere by substituting the values in the formula :

$\quad\implies{\pmb{\sf{V = \dfrac{2}{3} \pi {r}^{3}}}}$

• V = Volume
• π = 22/7
• r = radius

$\quad\implies{\sf{V = \dfrac{2}{3} \pi {r}^{3}}}$

$\quad{\implies{\sf{V = \dfrac{2}{3} \times \dfrac{22}{7} \times {(17.15)}^{3}}}}$

$\quad{\implies{\sf{V \approx \dfrac{2}{3} \times \dfrac{22}{7} \times (5044.20)}}}$

$\quad{\implies{\sf{V \approx \dfrac{2}{3} \times \dfrac{22}{7} \times 5044.20}}}$

$\quad{\implies{\sf{V \approx\dfrac{2 \times 22}{3 \times 7} \times 5044.20}}}$

$\quad{\implies{\sf{V \approx\dfrac{66}{21} \times 5044.20}}}$

$\quad{\implies{\sf{V \approx\dfrac{66}{\cancel{21}} \times \cancel{5044.20}}}}$

$\quad{\implies{\sf{V \approx 66 \times 240.2}}}$

$\quad{\implies{\sf{\underline{\underline\pink{V \: \approx \: 15853.2 \: {m}^{3}}}}}}$

Hence, the volume of hemisphere is 15853.2 m³.

$\rule{300}{2.5}$