A three-dimensional geometric shape that has a circular base and a sharp point (vertex) is known as a cone. You must have seen a birthday cap or eaten ice cream with a circular base and a sharp point, all these are real-life examples of the cone. The surface area of cone can be defined as the total amount of area or region that has been occupied by the cone inside it. Mathematically, the surface area of a cone is classified into two types. One is the total surface area of the cone and the latter is the curved surface area of the cone. The formula is given for the total surface area of the cone (TSA) πr(r + l) where ‘r’ is the radius of the cone, ‘l’ is the slant height of the cone. Likewise, the formula for the curved surface area (CSA) is πrl where, ‘r’ is the radius of the cone, ‘l’ is the slant height of the cone. However, the resultant value for both the formulas is written in square units. We may solve some examples related to the surface and curved area of the cone in the coming sections.
Examples based on the Surface Area of Cone
To recall, the surface area of a cone is classified into two types. One is the total surface area of the cone and the latter is the curved surface area of the cone. Some examples related to the TSA AND CSA are mentioned below.
Example 1: Find the curved surface area of the cone if the slant height and radius are 8 cm and 4 cm respectively. Take the value of π as 22/7.
Solution:
Given that,
The slant height of the cone = 8 cm
The radius of the cone = 4 cm
Using the formula for the curved surface area of cone = πrl.
22/7 * 4 cm * 8 cm = 22/7 * 32 cm square units.
22/7 * 32 = 100.48 cm square units.
Hence, the curved surface area of a cone is = 100.48 cm square units.
Example 2: Find the total surface area of the cone if the slant height is 6 cm and radius is 8 cm? Take the value of π as 3.14.
Solution:
Given that,
The slant height of the cone = 6 cm
The radius of the cone = 8 cm
Using the formula for the total surface area of cone = πr(r + l)
3.14 * 8 cm ( 8 cm + 6 cm) = 3.14 * 8 cm ( 14 cm) .
3.14 * 8 cm ( 14 cm) = 3.14 * 8 * 14.
3.14 * 8 * 14 = 351.68 cm square units.
Therefore, the total surface area of the cone is equivalent to 351.68 square units.
Surface Area of Sphere
A geometrical shape or object which does not contain any vertices or edges is defined as the sphere. A sphere can also be written as a three-dimensional object which is round shaped. One interesting fact about the sphere is that all the points are equidistant from the center. If we make a point on a sphere and measure it from the center, it will be equivalent to the length of other points. A sphere can be observed in various real-life objects. Our earth is often considered a sphere. However, it is a spheroid. The surface area of a sphere can be defined as the total region or area occupied by the sphere inside it. Mathematically, the surface area of sphere. is 4πr. πr where ‘r’ is the radius of the sphere. The resultant value of the surface area of a sphere is always written in square units. We shall cover some examples based on them in the next section.
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