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Math՚s: Meaning of Surface Area and Volume: Cuboids and Cubes
Meaning of Surface Area and Volume
The terms surface area and volume are used in connection with solid figures.
- The surface constituting the solid is called the surface area of the solid figure. Surface area is measured in square units such as etc.
- The space region enclosed by the solid figure is called the volume of the solid figure. Volume is measured in cubic units such as etc.
Cuboids and Cubes
Cuboids- Cuboid is a solid figure with six rectangular flat faces (ABCD, EFGH, DCGH, ABFE, BCGF & ADHE) ; twelve edges (AB, BC, CD, AD, EF, FG, GH, EH, AE, BF, CG & DH) and eight vertices (A, B, C, D, E, F, G & H) . Ex- Match Box, Brick etc.
At each vertex, three edges meet. One of these three edges is taken as the length , the second as the breadth and third is taken as the height (or thickness or depth) of the cuboid.
- Surface Area: Total Surface Area-
- Lateral Surface Area:
- Volume:
- Diagonal:
Cubes- Cube is a special type of cuboid where all the six faces are of square shapes of equal sides .
- Surface Area: Total Surface Area-
- Lateral Surface Area:
- Volume:
- Diagonal:
Right Circular Cylinder
A solid figure having a curved lateral surface closed with two flat circular ends (top & bottom faces) is known as a right circular cylinder.
Surface Area- Curved/Lateral:
Total Surface Area:
Volume:
Volume of Hollow Cylinder:
1. Find the edge of a cube whose volume is 3375 cm3. Also, find its surface area.
Solution- Let the edge of the cube be ,
Then,
2. Find the length and surface area of a wooden plank of width 3 m, thickness 75 cm and volume 33.75 m3.
Solution- The units of all the dimensions have to be same, so thickness of the wooden plank will be converted into meter.
Let the length of the wooden plank be .
3. Volume of a right circular cylinder is 3080 cm3 and radius of its base is 7 cm. Find the curved surface area of the cylinder.
Solution- Let the height of the cylinder be cm