Question

A cube of 25 cm side is divided into 125 smaller cubes of equal volume. Find the side of smaller cubes.

• A. 2 cm
• B. 3 cm
• C. 5 cm
• D. 6 cm

Hint:

In cube problems, find the volume of the large cube and divide it by the number of smaller cubes to get the volume of each. Then, take the cube root to find the side length.

Answer 1

The Correct Option is C

Step 1: The volume of the large cube is \( V = \text{side}^3 = 25^3 = 15625 \, \text{cm}^3 \). Step 2: The large cube is divided into 125 smaller cubes, so the volume of each smaller cube is: \[ V_{\text{small}} = \frac{15625}{125} = 125 \, \text{cm}^3 \] Step 3: The side of each smaller cube is the cube root of 125: \[ \text{Side of smaller cube} = \sqrt[3]{125} = 5 \, \text{cm} \] Thus, the side of each smaller cube is 5 cm.