Sixteen glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 20 cm `xx` 10 cm `xx` 10 cm and then the box is filled with water. Find the volume of water filled in the box.

Answer

To find the volume of water filled in the cuboidal box after packing 16 glass spheres, we can follow these steps:

### Step 1: Calculate the Volume of the Cuboidal Box
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the box are \( 20 \, \text{cm} \times 10 \, \text{cm} \times 10 \, \text{cm} \):
\[ V = 20 \times 10 \times 10 = 2000 \, \text{cm}^3 \]

### Step 2: Calculate the Volume of One Sphere
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Given the radius \( r = 2 \, \text{cm} \):
\[ V = \frac{4}{3} \pi (2)^3 = \frac{4}{3} \pi (8) = \frac{32}{3} \pi \, \text{cm}^3 \]
Using \( \pi \approx 3.14 \):
\[ V \approx \frac{32}{3} \times 3.14 \approx 33.51 \, \text{cm}^3 \]

### Step 3: Calculate the Volume of 16 Spheres
Now, to find the total volume of 16 spheres:
\[ \text{Total Volume} = 16 \times \frac{32}{3} \pi \approx 16 \times 33.51 \approx 536.16 \, \text{cm}^3 \]

### Step 4: Calculate the Volume of Water
The volume of water filled in the box is the volume of the box minus the volume occupied by the spheres:
\[ \text{Volume of Water} = \text{Volume of Box} - \text{Volume of Spheres} \]
Substituting the values:
\[ \text{Volume of Water} = 2000 \, \text{cm}^3 - 536.16 \, \text{cm}^3 \approx 1463.84 \, \text{cm}^3 \]

### Final Answer
The volume of water filled in the box is approximately \( 1463.84 \, \text{cm}^3 \).

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