A paper cone has a base diameter of 8cm and a height of 3cm. Calculate the curved surface area of the cone in terms of p¹ (pie)
the slant height (s) is ... s^2 = √[(8/2)^2 + 3^2]
... s is the radius of the circle the cone was made from
the area of the source circle is ... π s^2
the circumference of the source circle is ... 2 π s
the circumference of the cone base is ... 8 π
the curved surface area of the cone is ... [(8 π) / (2 π s)] * π s^2
and that's pi, not pie
The formula for the curved surface area of a cone is given by:
CSA = π * r * l
where r is the radius of the base and l is the slant height of the cone.
To find the slant height, we can use the Pythagorean Theorem:
l = √(r^2 + h^2)
Given that the base diameter is 8 cm, the radius (r) would be half of that, which is 8/2 = 4 cm. The height (h) is given as 3 cm.
Now, let's substitute these values into the formulas:
l = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 cm
CSA = π * 4 * 5 = 20π cm²
Therefore, the curved surface area of the cone is 20π cm².
To find the curved surface area of a cone, you first need to calculate the slant height. The slant height can be determined using the Pythagorean theorem, which states that the square of the slant height is equal to the sum of the square of the height and the square of the radius.
Given:
Base diameter = 8 cm
Radius = diameter/2 = 8/2 = 4 cm
Height = 3 cm
Using the Pythagorean theorem:
Slant height² = Radius² + Height²
Slant height² = 4² + 3²
Slant height² = 16 + 9
Slant height² = 25
Taking the square root of both sides:
Slant height = √25
Slant height = 5 cm
Now that we have the slant height, we can calculate the curved surface area of the cone. The curved surface area of a cone is given by the formula:
Curved Surface Area = π * radius * slant height
Substituting the given values:
Curved Surface Area = π * 4 * 5
Curved Surface Area = 20π cm²
Therefore, the curved surface area of the cone is 20π cm².