The volume of a cube is 2197 cm³. What is its lateral surface area (in cm²) ?

The correct option is 676.

Step 1: Find the side length of the cube.
Let the side length of the cube be $a$ cm.
The volume of a cube is given by the formula:

$\text{Volume}=a^3$

Given that the volume of the cube is 2197 cm³:

$a^3=2197$

Taking the cube root on both sides:

$a=\sqrt[3]{2197}$

Since ${13}^3=2197$, we find:

$a=13\text{cm}$

Step 2: Calculate the lateral surface area of the cube.
The lateral surface area (LSA) of a cube consists of the area of its 4 side faces and is given by the formula:

$\text{LSA}=4a^2$

Substitute $a=13$ into the formula:

$\text{LSA}=4\times {\left(13\right)}^2$

$\text{LSA}=4\times 169$

$\text{LSA}=676{\text{cm}}^2$

Thus, the lateral surface area of the cube is 676 cm².