Question

The volume of a solid hemisphere is $56\frac{4}{7} cm^3$. What is its total surface area (in cm²)? (Take $\pi=\frac{22}{7}$)

• A. $$\frac{495}{7}$$
• B. $$\frac{396}{7}$$
• C. $$\frac{594}{7}$$
• D. $$\frac{494}{7}$$

Answer 1

Answer:

$$\frac{594}{7}$$

Given:

The volume of a solid hemisphere is 56\frac{4}{7} cm^3

Take $\pi=\frac{22}{7}$

Formula used:

The volume of the solid hemisphere $=\frac{<span style="color: inherit">2}{3}</span>\pi{r^3}$

The total surface area of the solid hemisphere = 3πr²

Where, 

r, is the radius of the hemisphere

Calculation:

According to the question, the required figure is:

The volume of the solid hemisphere,

$\frac{2}{3}\pi{r^3}=56\frac{4}{7}$

$\frac{2}{3}\times{\frac{22}{7}}\times{r^3}=\frac{396}{7}$

$\frac{2}{3}\times{22}\times{r^3}=396$

$r^3=\frac{396\times{3}}{2\times{22}}$

$r^3=27$

$r=3$

Now, 

The total surface area of the solid hemisphere $=3\times{\frac{22}{7}}\times{32}=\frac{594}{7}cm^3$