One laddoo with a radius of 5 cm belongs to a shopkeeper. How many laddoos of radius 2.5 cm may be created from the same one laddoo?

The correct answer is 8.

Step-by-Step Explanation:

A laddoo is spherical in shape. The volume of a sphere of radius $r$ is calculated using the formula:

$V=\frac{4}{3}\pi r^3$

Given Data:
Radius of the original (large) laddoo, $R_1=5\text{cm}$
Radius of each smaller laddoo, $R_2=2.5\text{cm}$

Step 1: Calculate the Volume of the Original Laddoo

$V_1=\frac{4}{3}\pi {\left(5\right)}^3=\frac{4}{3}\pi \times 125{\text{cm}}^3$

Step 2: Calculate the Volume of One Smaller Laddoo

$V_2=\frac{4}{3}\pi {\left(2.5\right)}^3=\frac{4}{3}\pi \times 15.625{\text{cm}}^3$

Step 3: Calculate the Total Number of Smaller Laddoos
The number of smaller laddoos ($N$) that can be created is equal to the volume of the large laddoo divided by the volume of one smaller laddoo:

$N=\frac{V_1}{V_2}$

$N=\frac{\frac{4}{3}\pi {\left(5\right)}^3}{\frac{4}{3}\pi {\left(2.5\right)}^3}$

Canceling out the common term $\frac{4}{3}\pi$ from the numerator and denominator gives:

$N={\left(\frac{5}{2.5}\right)}^3$

$N=2^3=8$

Therefore, 8 laddoos of radius 2.5 cm can be created from the original laddoo.