Calculate the total surface area of a cone of height 12cm and base radius 5cm. [Take π = 22/7]
Answer Details
To find the total surface area of a cone, we need to add the area of the base and the curved surface area.
Given that the base radius is 5cm, we can find the base area by using the formula for the area of a circle:
Area of base = πr² = π(5)² = 25π
To find the curved surface area, we need to first find the slant height of the cone. We can use the Pythagorean theorem to find this value:
l = √(r² + h²) = √(5² + 12²) = √169 = 13cm
Now, we can find the curved surface area using the formula:
Curved surface area = πrl
Curved surface area = π(5)(13) = 65π
Therefore, the total surface area of the cone is:
Total surface area = Base area + Curved surface area
Total surface area = 25π + 65π = 90π
Using the approximation π = 22/7, we get:
Total surface area = 90π = 90(22/7) = 282.8571... cm²
Rounding off to one decimal place, we get:
Total surface area ≈ 282.9 cm²
Therefore, the correct option is 4) 282 6/7cm².