A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream cones of radius 2 cm and height 7 cm up to its brim . How many children will get the ice-cream cones ?

Options

A. 163
B. 263
C. 363
D. 463

Explanation

To solve the problem, we need to find out how many ice-cream cones can be filled with the volume of a cubical ice-cream brick. Let's go through the solution step by step.

### Step 1: Calculate the Volume of the Cubical Ice-Cream Brick
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of an edge of the cube.

Given that the edge of the cube is 22 cm:
\[ V = 22^3 = 22 \times 22 \times 22 \]
Calculating this:
\[ 22 \times 22 = 484 \]
\[ 484 \times 22 = 10648 \text{ cm}^3 \]
So, the volume of the ice-cream brick is \( 10648 \text{ cm}^3 \).

### Step 2: Calculate the Volume of One Ice-Cream Cone
The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.

Given that the radius \( r \) is 2 cm and the height \( h \) is 7 cm:
\[ V = \frac{1}{3} \pi (2^2) (7) \]
Calculating this:
\[ 2^2 = 4 \]
\[ V = \frac{1}{3} \pi (4) (7) = \frac{28}{3} \pi \text{ cm}^3 \]

### Step 3: Calculate the Number of Cones that can be Filled
To find the number of cones \( n \) that can be filled, we divide the volume of the ice-cream brick by the volume of one cone:
\[ n = \frac{\text{Volume of the cube}}{\text{Volume of one cone}} = \frac{10648}{\frac{28}{3} \pi} \]
This simplifies to:
\[ n = 10648 \times \frac{3}{28 \pi} \]
Calculating \( 10648 \div 28 \):
\[ 10648 \div 28 = 380.2857 \text{ (approximately)} \]
Now multiplying by 3:
\[ n \approx 380.2857 \times 3 = 1140.8571 \]
Finally, dividing by \( \pi \) (approximately 3.14):
\[ n \approx \frac{1140.8571}{3.14} \approx 363.33 \]
Since \( n \) must be a whole number, we round down to get \( n = 363 \).

### Final Answer
Thus, the number of children that can get the ice-cream cones is **363**.

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