Ram waritto build a solid cube of 15 cm side. How many pieces are required of 5 cm side ?

Options

A. 20
B. 30
C. 27
D. 22

Answer

To solve the problem of how many pieces of a smaller cube (5 cm side) are required to build a larger cube (15 cm side), we can follow these steps:

### Step 1: Calculate the volume of the larger cube.
The formula for the volume \( V \) of a cube is given by:
\[ V = L^3 \]
where \( L \) is the length of a side of the cube.

For the larger cube with a side of 15 cm:
\[ V_{\text{larger}} = 15^3 = 15 \times 15 \times 15 \]
Calculating this:
\[ 15 \times 15 = 225 \]
Then,
\[ 225 \times 15 = 3375 \text{ cm}^3 \]
So, the volume of the larger cube is \( 3375 \text{ cm}^3 \).

### Step 2: Calculate the volume of the smaller cube.
Using the same formula for the volume of a cube, we calculate the volume for the smaller cube with a side of 5 cm:
\[ V_{\text{smaller}} = 5^3 = 5 \times 5 \times 5 \]
Calculating this:
\[ 5 \times 5 = 25 \]
Then,
\[ 25 \times 5 = 125 \text{ cm}^3 \]
So, the volume of the smaller cube is \( 125 \text{ cm}^3 \).

### Step 3: Determine the number of smaller cubes needed.
To find out how many smaller cubes fit into the larger cube, we divide the volume of the larger cube by the volume of the smaller cube:
\[ \text{Number of smaller cubes} = \frac{V_{\text{larger}}}{V_{\text{smaller}}} = \frac{3375}{125} \]
Calculating this:
\[ \frac{3375}{125} = 27 \]
Thus, Ram will need **27 pieces** of the smaller cube to build the larger cube.

### Final Answer:
Ram requires **27 pieces** of 5 cm side cubes to build a solid cube of 15 cm side.

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