A hemispherical bowl is 88 cm round the brim. Assuming it to be full, how many persons may be served from it in hemispherical glasses, 7 cm in diameter at the top? (Where π=722 ).

The correct option is 64.

Step 1: Find the radius of the hemispherical bowl.
The circumference around the brim of the hemispherical bowl is given as 88 cm.
The formula for the circumference of the circular brim is:

$\text{Circumference}=2\pi R$

where $R$ is the radius of the hemispherical bowl.
Substitute the given circumference of 88 cm and $\pi =\frac{22}{7}$:

$2\times \frac{22}{7}\times R=88$

$\frac{44}{7}\times R=88$

$R=88\times \frac{7}{44}$

$R=2\times 7=14\text{cm}$

Step 2: Find the radius of the hemispherical glass.
The diameter at the top of each hemispherical glass is 7 cm.
Therefore, the radius $r$ of each glass is:

$r=\frac{\text{Diameter}}{2}=\frac{7}{2}=3.5\text{cm}$

Step 3: Formulate the equation for the number of persons served.
The volume $V$ of any hemisphere with radius $x$ is given by:

$V=\frac{2}{3}\pi x^3$

The total number of persons who can be served equals the volume of the full bowl divided by the volume of one glass:

$\text{Number of persons}=\frac{V_{\text{bowl}}}{V_{\text{glass}}}=\frac{\frac{2}{3}\pi R^3}{\frac{2}{3}\pi r^3}$

Canceling the common factor $\frac{2}{3}\pi$ from both numerator and denominator:

$\text{Number of persons}={\left(\frac{R}{r}\right)}^3$

Step 4: Calculate the final value.
Substitute $R=14\text{cm}$ and $r=3.5\text{cm}$ into the simplified ratio:

$\text{Number of persons}={\left(\frac{14}{3.5}\right)}^3$

$\text{Number of persons}=4^3=64$

Thus, 64 persons may be served from the bowl.