Three cubes each of volume 125 cm are joined end to end to form a cuboid. find the total surface area of cuboid.
14 * 25 see below
To find the total surface area of the cuboid formed by joining three cubes, we need to consider the individual surface areas of each cube and the additional surface areas created by joining them together.
1. Surface area of each cube:
Since each cube has a volume of 125 cm³, we can find the length of each side by taking the cube root of the volume: ∛125 = 5 cm.
The total surface area of each cube is given by the formula: 6 * (side length)².
So, the surface area of each cube is: 6 * (5 cm)² = 6 * 25 = 150 cm².
2. Additional surface areas when cubes are joined:
When three cubes are joined together, three pairs of faces will be adjacent to form the new cuboid shape.
The additional surface area is given by the sum of the areas of these exposed faces.
For each pair of adjacent faces, the common side length is 5 cm.
So, the additional surface area is: 3 * (side length)² = 3 * (5 cm)² = 3 * 25 = 75 cm².
3. Total surface area of the cuboid:
To find the total surface area, we need to add up the surface areas of the individual cubes and the additional surface areas created by joining them together.
Total surface area = (Surface area of each cube) + (Additional surface area when cubes are joined)
Total surface area = 3 * (Surface area of each cube) + (Additional surface area when cubes are joined)
Total surface area = 3 * 150 cm² + 75 cm²
Total surface area = 450 cm² + 75 cm²
Total surface area = 525 cm².
So, the total surface area of the cuboid formed by joining three cubes is 525 cm².