Surface Area and Volume of 3D: Cube, Cuboid Surface area and volume are crucial concepts in quantitative aptitude for understanding the amount of space an ob...
Surface area and volume are crucial concepts in quantitative aptitude for understanding the amount of space an object occupies and the amount of surface area it has.
Surface Area:
Imagine a 2D shape like a rectangle. Its surface area is the sum of the areas of its four sides. Similarly, the surface area of a 3D shape like a cube or cuboid is the sum of the areas of its six faces.
Cuboid
A cuboid is a 3D shape with rectangular faces. Its surface area is equal to the sum of the areas of all its faces. The area of a face is equal to the length times the width of that face.
Cube
A cube is a 3D shape with equal sides. Its surface area is equal to the sum of the areas of all its faces. The area of a face is equal to the side length squared.
Examples:
Surface area:
A cube with side length 3 cm has a surface area of 9 cm².
A rectangular box with dimensions 5 cm x 3 cm x 2 cm has a surface area of 30 cm².
Volume:
A cuboid with side length 4 cm has a volume of 64 cm³.
A cube with side length 5 cm has a volume of 25 cm³.
Key Differences:
Surface area is the "total area" of a 3D shape, including all faces, while volume is the "interior space" occupied by a 3D shape.
Surface area is always greater than or equal to the volume, as the surface area includes the areas of all faces, while the volume only includes the space inside the shape.
Understanding surface area and volume is crucial for various applications, such as finding the total area of a surface for painting, finding the volume of a solid for construction, and calculating the amount of material needed to make a 3D object