Final answer:
To calculate the surface area of the cuboid formed by stacking four 20 cm cubes, compute the area of each set of identical faces and add them together to get a total surface area of 7200 cm².
Step-by-step explanation:
To find the surface area of the resulting cuboid when Hema places 4 cubes each with an edge of 20 cm one above the other, we first need to realize that in this arrangement, we will have a taller cuboid with one dimension (height) that is four times longer than the individual cube's side. So, the dimensions of the resulting cuboid will be 20 cm by 20 cm by 80 cm. To find the surface area of a cuboid, we add up the areas of all six faces. Here's the step-by-step calculation:
- Calculate the area of the three different pairs of faces: the bottom and top (20 cm × 20 cm), the front and back (20 cm × 80 cm), and the sides (20 cm × 80 cm).
- Multiply each area by 2, since there are two of each face.
- Add up the total areas of the pairs to get the total surface area.
Area of top and bottom faces: 20 cm × 20 cm = 400 cm² × 2 = 800 cm²
Area of front and back faces: 20 cm × 80 cm = 1600 cm² × 2 = 3200 cm²
Area of side faces: 20 cm × 80 cm = 1600 cm² × 2 = 3200 cm²
Total surface area = 800 cm² + 3200 cm² + 3200 cm² = 7200 cm²
The total surface area of the cuboid made by stacking the four cubes is 7200 cm².