Surface Area of Cone Examples
Example 1: Find the total surface area of a cone if its radius is 15 cm and its slant height is 10 cm. (Use π = 3.14.formula)
Solution:
Given
- Radius of cone (r) = 15 cm
- Slant height (l) = 10 cm
We know that,
Total Surface Area of Cone = πr (r + l) square units
= (3.14) × 15 × (15 + 10)
= 1,177.5 sq. cm
Hence, total surface area of cone is 1,177.5 sq. cm.
Example 2: What is the height of a cone if its radius is 14 units and its curved surface area is 1100 square units? (Use π = 22/7)
Solution:
Given
- Radius of cone (r) = 14 units
- Curved surface area of the cone = 1100 square units
Let the slant height of the cone be “l” and the height of the cone be “h”.
We know that,
Curved surface area of the cone = πrl square units
⇒ 1100 = (22/7) × 14 × l
⇒ 44 × l = 1100
⇒ l = 1100/44 = 25 units
We know that,
slant height (l) = √(h2 + r2)
⇒ h = √(l2 – r2)
= √(252 – 142) = √429 = 20.71 units
Thus, height of cone is 20.71 units.
Example 3: Determine the slant height of the cone if the total surface area of the cone is 525 sq. cm and the radius is 7 cm. (Use π = 22/7)
Solution:
Given
- Radius of cone (r) = 7 cm
- Total surface area of the cone = 525 sq. cm
Let, slant height of cone be “l”
We know that,
Total surface area of Cone = πr (r + l) square units
⇒ (22/7) × 7 × (7 + l) = 525
⇒ 22 × (7 + l) = 525
⇒ 7 + l = 23.86
⇒ l = 16.86cm
Therefore, slant height of cone is 16.86 cm.
Surface Area of Cone
Surface Area of a Cone is the total area encompassing the circular base and the curved surface of the cone. A cone has two types of surface areas. If the radius of the base is ‘r’ and the slant height is ‘l’, we use two formulas:
- Total Surface Area (TSA) of the cone = πr(r + l)
- Curved Surface Area (CSA) of the cone = πrl
In this article, we will talk about the surface area of the cone, including the formulas for Total Surface Area and Curved Surface Area, with the help of solved examples.
Table of Content
- What is Surface Area of a Cone?
- Surface Area of Cone Formula
- Curved Surface Area of Cone
- Total Surface Area of Cone
- Derivation of Surface Area of Cone Formula
- Surface Area of Cone and Height
- Surface Area of Cone Examples
- Surface Area of Cone Class 9 NCERT