The diameter of the base of a cone is 10.5 cm and its length height its slant height is 10 centimeter the curved surface area is
The diameter of the base of a cone is 10.5 cm and its length height its slant height is 10 centimeter the curved surface area is
the curved surface is a portion of a Circle
the slant height is the radius of the Circle
the circumference of the base of the cone
... is a portion of the circumference of the Circle
area (A) of the Circle ... π * 10^2 = 100 π cm^2
circumference of the Circle ... π * 20 cm
circumference of the base of the cone ... π * 10.5 cm
curved surface area of the cone ... [(10.5 π) / (20 π)] * 100 π cm^2
To find the curved surface area of a cone, we need to use the formula:
Curved Surface Area = π * r * l
Where:
- π represents the mathematical constant pi, approximately equal to 3.14159
- r is the radius of the base of the cone
- l is the slant height of the cone
Given that the diameter of the base is 10.5 cm, we can find the radius by halving the diameter:
Radius (r) = Diameter / 2 = 10.5 cm / 2 = 5.25 cm
Now, since the slant height (l) is given as 10 cm, we have all the values we need to calculate the curved surface area:
Curved Surface Area = π * 5.25 cm * 10 cm
Calculating this, we get:
Curved Surface Area = 3.14159 * 5.25 cm * 10 cm
Curved Surface Area ≈ 164.93355 cm²
Therefore, the curved surface area of the given cone is approximately 164.93355 square centimeters.