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An important difference between area and volume depends upon the region covered by the object. Area is used for calculating two-dimensional objects, whereas volume is used for calculating a three-dimensional object.
- Finding the key difference between area and volume is essential in the field of geometry.
- As we know, geometry is the study of shapes, dealing with solid and plane shapes.
- We calculate various terms associated with shapes, such as height, volume, width, area, perimeter, length, etc.
- Area and volume are two essential concepts used in our daily life.
- We see many shapes around, like circles, squares, polygons, rectangles, etc.
- Every shape has its unique measurements and properties.
- Therefore, each shape has a different area and volume, depending on its measurement.
Key Terms: Difference between Area and Volume, Area, Volume, Geometry, Circles, Square, Polygons, Rectangles, Difference of Area and Volume of Shapes, Parallelogram, Hexagon
What is Area?
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The area is the measurement of the region covered by any 2-dimensional geometric shapes. Every shape has different areas. For instance, the area of a square is different from the area of a rectangle.
- It is linked to the outer space.
- The area of a shape is calculated in square (sq) units such as square inches, square feet, etc
- It is used to measure the number of unit squares that cover the surface of a closed figure.
- If two figures have similar shapes, they don't need to have the same area unless they have the same dimension.
- The 2D shapes include square, circle, hexagon, rectangle, pentagon, triangle, parallelogram, etc.
- Therefore, all these figures have different areas.
Example of What is Area?Example: We can see an example, if you want to paint a rectangular wall of your house, then you need to know the area of a wall so that you know how much amount of paint is required to paint the wall to calculate the cost of painting. |
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What is Volume?
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The volume of an object is defined as the measurement of the amount of space occupied by a 3-dimensional object. It is the product of all three dimensions and is expressed in cubic units.
- For each 3-dimensional shape, such as cylinder, cube, cone, sphere, cuboid, etc., the volume is different.
- The capacity of an object is the volume of the substance that its interior can accommodate.
- The interior of the object can accommodate is called the capacity of the hollow.
- It is measured by counting the number of unit cubes it contains.
Example of What is Volume?Example 1: Suppose the volume of a cube is measured by the product of its height, length, and breadth. The interior of a hollow object can be filled with a liquid or air that takes the shape of the object. Example 2: How much oil can be stored in a cylindrical vessel having a radius of 2m, and height 7m? Ans: Radius of the cylinder = 2m Height of the cylinder = 7 m Volume of the cylinder = π r2 h Volume = 22 X2 X2 X 7/ 7 Volume = 88 m3 1 m3 = 1000 l 88 m3 = 88000 L |
What is the differences between Area and Volume?
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Some of the differences between area and volume in mathematics are:
| Area | Volume |
|---|---|
| The area is defined as the space occupied by a 2-dimensional object. | The volume is the amount of space occupied by a 3-dimensional object. |
| It is expressed in a square unit. | It is expressed in the cubic unit. |
| This is a plane figure. | This is a solid figure. |
| The area covers outer space. | The volume covers the inner capacity. |
| It is calculated for 2 dimensions. | It is measured in 3 dimensions, i.e. Length, breadth, and height. |
| Examples: circle, square, rectangle, etc. | Examples: cube, sphere, cylinder, etc. |
Difference of Area and Volume of Shapes
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Let us look at the areas of different shapes here:
| Name of the shapes | Variables | Area of the shape |
|---|---|---|
| Triangle | B = base H = height | \(\frac{1}{2}\) × base × height |
| a = base 1 b = base 2 h = vertical height | \(\frac{1}{2}\) (sum of parallel side) × height | |
| Semicircle | r = radius of the circle | \(\frac{1}{2} \pi r^2\) |
| a= side of the rhombus h = height | a × h | |
| Circle | r = radius of the circle= 22/7 or 3.1416 | πr2 |
| Square | a = sides of the square | a2 |
| Rectangle | l = length w = width | l × w |
| Parallelogram | a = side b = base h = vertical height | b × h |
Now, let us look at the volume of different shapes here:
| Name of the Shape | Abbreviation Used | Volume |
|---|---|---|
| Sphere | r = radius | 4/3πr3 |
| Right circular cylinder | r = radius h = height | πr2h |
| Right circular cone | r = radius l = length | \(\frac{1}{2}\)πr2h |
| Cube | a = length of the side | a3 |
| Cuboid | l = length b = breadth h = height | l × b × h |
| r = radius | \(\frac{2}{3}\)(πr3) | |
| - | \(\frac{1}{3}\) (Area of the base) × height | |
| - | Area of base × height |
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Things to Remember
- Difference between area and volume measurement of the region covered by the figure.
- Area can be defined mainly for 2D figures, such as triangles, trapezoids, Semicircles, rhombus, circles, and Parallelograms.
- Volume can be defined for 3D figures, such as Spheres, right circular cylinders, right circular cones, Cubes, Cuboids, Hemispheres and right prism.
- We can define an area for three dimensional objects, but it would be a surface area, which is known as the area of the surface of 3D figures.
- Volume is used in determining the density, mass, and properties of objects and substances.
Sample Questions
Ques: What is the volume of the cube if the edge length is 10cm? (2 marks)
Ans: We have, edge length, a = 10cm
Volume of cube = a3 [Formula]
So, volume of cube = 103
= 10 ×10 × 10 = 1000
So, the volume of the cube is 1000cm3.
Ques: What is the area of a rectangle with a length of 10 cm and a width of 5 cm? (2 marks)
Ans: We have, length of rectangle = 10cm
Width of rectangle = 5 cm
Area of the rectangle = length × width [Formula]
So, the area of the rectangle = 10 × 5
= 10 × 5 = 50
So, the area of the rectangle is 50cm2.
Ques: What is the volume of a cubic box if its side is 8cm? (2 marks)
Ans: We have, side of the box, a = 8cm
Volume of cube = a3 [Formula]
So, volume of cube = 83
= 8 × 8 × 8 = 512
So, the volume of cubic box is 512cm3.
Ques: What is the area of a square plot if the side is 7cm? (2 marks)
Ans: We have, side of the square plot, s = 7cm
Area of square = a2 [Formula]
So, area of square = 72
= 7 × 7 = 49
So, the area of the square plot is 49cm.
Ques: Is the cube a square? (2 marks)
Ans: A square is a two-dimensional shape that has w dimensions of length and breadth, while a cube is a 3-dimensional shape that has 3 dimensions of height, length, and breadth. The side faces of a cube are formed by the square and it has 4 verticals and 4 sides, while a cube has 8 verticals and 12 sides. From these properties, we can say that the basic difference between a cube and a square is of dimensions.
Ques: What is the volume of a sphere having a radius of 3 cm? (3 marks)
Ans. Radius of sphere r = 7cm
Volume of a sphere = V = 4πr3/3 cubic units
V = 4/3 × 3.14 × 73
V = 4/3 × 3.14 × 7 × 7 × 7
V = 1436.04 cm3
Hence the volume of given sphere is 1436.04 cubic cm.
Ques: Calculate the area of the triangle whose base is 21 cm and height is 10 cm? (2 marks)
Ans: Area of a triangle = ½xbxh
Given, base = 21 cm & height = 10 cm
Area = ½ x 21 x 10 = 105 cm².
Ques: Calculate the breadth of a rectangular plot of land, if its area is 360 square meters and the length is 120 m? (2 marks)
Ans. Area = 360 square m (given)
Length (l) = 120 m
Area of a rectangle = l x b
360 = 120 x b
b = 360/120 = 3 m
Ques: From a rectangular sheet of paper of dimensions 9 cm × 4 cm, a square piece of dimension 1 cm × 2 cm. What will be the ratio of the areas of the two figures? (3 marks)
Ans: Length = 9 cm
Breadth = 4 cm
Area of the sheet = l × b = 9 cm × 4 cm = 36 cm²
Area of the square piece = 1 cm × 2 cm = 2 cm²
Ratio of areas of two figures = 36 cm² : 2 cm² = 18 : 1
Ques: Two cubes of edge 4 cm are joined to form a cuboid. Find the total surface area of the cuboid? (2 marks)
Ans: When two cubes are joined end to end, then
Length of the cuboid = 4 + 4 = 8 cm
Breadth of the cuboid = 4 cm
Height of the cuboid = 4 cm
Total surface area of the cuboid = 2 (lb + bh + hi)
= 2(8 x4 + 4×4 + 4×8)
= 2(32 + 16 + 32) = 2(80) = 160 cm2
Ques: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 12 m? (Assume π = 22/7) (2 marks)
Ans: Radius of cone, r = 12/2 m = 6m
Slant height, l = 21 m
Formula: Total Surface area of the cone = πr(l+r)
Total Surface area of the cone = (22/7)×6×(21+6) m2
= 509.14m2
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