How do you derive the surface area of a cube?
How do you derive the surface area of a cube?
The total surface area of a cube is the area covered by all the six faces of a cube. The formula to find total surface area of a cube is given as, Total surface area = 6a2, where, ‘a’ is the edge length of the cube.
What is the formula for total surface area?
Variables:
| Surface Area Formula | Surface Area Meaning |
|---|---|
| SA=4πr2 | Find the area of the great circle and multiply it by 4. |
| SA=B+πrS | Find the area of the base and add the product of the radius times the slant height times PI. |
What is the formula of LSA and TSA of cube?
Cube and Cuboid Formulas
| Cube | Cuboid |
|---|---|
| Total Surface Area = 6(side)2 | Total Surface area = 2 (Length x Breadth + breadth x height + Length x height) |
| Lateral Surface Area = 4 (Side)2 | Lateral Surface area = 2 height(length + breadth) |
| Volume of cube = (Side)3 | Volume of the cuboid = (length × breadth × height) |
How do you work out SA of a cube?
To determine the surface area of a cube, calculate the area of one of the square sides, then multiply by 6 because there are 6 sides. This is the same as solving using the formula SA = 6s2. If you are given the surface area, you can determine the side length by working backwards.
What is TSA in math?
The total surface area (TSA) includes the area of the circular top and base, as well as the curved surface area (CSA).
What is the lateral surface area of the cube?
For a cube the lateral surface area would be the area of the four sides. If the edge of the cube has length a, the area of one square face Aface = a ⋅ a = a2. Thus the lateral surface of a cube will be the area of four faces: 4a2.
How do you find the lateral area and surface area of a cube?
In the case of a cube, the lateral surface area consists of the area of four of the cube’s sides added together, or 4 times the area of one of the cube’s sides. Thus, the lateral surface area of a cube can be found using the formula 4s^2, where s is the side length of the cube.
What is the surface area of a cube 3x3x3?
As you already know, a cube has six square faces. If each of those faces is 3 inches by 3 inches, then the area of each face is 3 × 3 = 9 square inches. And since there are six of them, the total surface area is 9 + 9 + 9 + 9 + 9 + 9 = 54 square inches.
How do you find surface area from volume?
It gives the proportion of surface area per unit volume of the object (e.g., sphere, cylinder, etc.). Therefore, the formula to calculate surface area to volume ratio is: SA/VOL = surface area (x2) / volume (x3) SA/VOL = x-1 , where x is the unit of measurement.
What is the meaning of TSA and LSA?
TSA or total surface area is the sum of areas of all the surfaces of an object. LSA or lateral surface area is the areas of the lateral surfaces of an object.
How to calculate the surface area of a cube?
Hence, surface area of the cube = 2 (l × l +l × l + l × l) = 2 x 3l2 = 6l2 Example: If the length of the side of the cube is 6 cm, then find its total surface area. Example: If the length of the side of the cube is 6 cm, then find its lateral surface area.
How is the surface area of a cuboid determined?
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces. Consider a cuboid having the length to be ‘l’ cm, breadth be ‘b’ cm and height be ‘h’ cm. Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces
What are the formulas for Cube and cuboid?
The formulas for cube and cuboid are defined based on their surface areas, lateral surface areas and volume. Cube. Cuboid. Total Surface Area = 6 (side)2. Total Surface area = 2 (Length x Breadth + breadth x height + Length x height) Lateral Surface Area = 4 (Side)2.
What’s the difference between total surface area and curved surface area?
The main difference between the total surface area (TSA) and curved surface area (CSA) is that TSA refers to the area of all the faces of the solid, whereas the CSA is the area of the curved region of the solid and this excludes the areas of top and bottom regions. Put your understanding of this concept to test by answering a few MCQs.