What is Surface Area?
The space occupied by the two-dimensional flat surface is just called area.
Surface area however, is defined as the sum of the areas of all the surfaces of a solid shape.
Types of Surface Area
- Total surface area (TSA): The total surface area is defined as the area of all the faces including the bottom and top faces of the object.
- Curved surface area (CSA): The curved surface area is defined as the area of all the faces excluding the bottom and top faces of the object.
Units of Surface Area
The surface area of any shape is measured in square units.
The standard unit is meter square. Others are centimeter square, millimeter square, etc.
What is Volume?
The volume of an object or shape is defined as the space enclosed by an object or the capacity to hold something.
Two-dimensional shapes do not have volume. Only, three-dimensional objects have volume.
Units of Volume
The volume of a solid is measured in cubic units.
The standard unit is meter cube. Others are centimeter cube, millimeter cube, inch cube etc.
Liter is a unit used to measure the volume of liquids.
1 liter = 1000 centimeter cube
Rapid Recall
Solved Examples
Example 1: Find the surface area of the cylinder.
Solution:
From the figure,
Height of the cylinder = 25 cm
Radius of the cylinder = 10 cm
We know that,
Surface area of the cylinder,
S = 2π\(r^2\) + 2πrh
= 2π(\(10^2\)) + 2π(10)(25 ) [Substitute 10 for r and 25 for h]
= 200π + 500π [add]
= 700π
= 700 × \(\frac{22}{7}\) [Substitute \(\frac{22}{7}\) for pi]
= 100 × 22 [multiply]
= 2200 \(cm^2\)
Hence, the surface area for the given cylinder is 2200 \(cm^2\).
Example 2: Find the volume of the cone.
Solution:
From the figure,
Height of the cone, h = 7 m
Radius of the cone, r = 3 m
We know that, volume of the cone
V = \(\frac{1}{3}\pi~r^2\)h [Volume of a cone formula]
= \(\frac{1}{3}\)π × 7 × \(3^2\) [Substitute 7 for h and 3 for r]
= 7 × 3 × π [multiply]
= 21π
= 21 × \(\frac{22}{7}\) [Substitute \(\frac{22}{7}\) for pi]
= 66 cubic meters
Hence, the volume of the given cone is 66 cubic meters.
Example 3: Find the volume of the sphere whose radius is 21 cm.
Solution:
Given, radius of the sphere (r) = 21 cm
We know that, volume of the sphere,
V = \(\frac{4}{3}\pi r^3\) [Volume of a sphere formula]
= \(\frac{4}{3}\)π × \((21)^3\) [Substitute 21 for r]
= \(\frac{4}{3}~\times~\frac{22}{7}~\times~21^3\) [Substitute \(\frac{22}{7}\) for π]
= 38808 \(cm^3\) [Simplify]
Hence, the volume of the sphere is 38808 \(cm^3\).
Surface area is defined as the sum of the areas of all the closed surfaces of a solid. While the space occupied by a two-dimensional flat surface is called area and not surface area.
Shapes like a square, a triangle, a circle and a semicircle, are a few examples of two dimensional shapes.
Solid shapes such as cylinders, spheres, cubes and cuboids are some examples of three-dimensional shapes.
The volume of an object or shape is defined as the space enclosed by an object or the capacity to hold something.
To measure surface area, we use units like meter square, centimeter square, millimeter square, etc.
To measure volume, units such as meter cube, centimeter cube, millimeter cube, etc. are used.