A cone has a base diameter of 8cm and height of 3cm calculate the curved surface area of the cone in terms of pie
20piecmsquare
now do it again in terms of pi
To calculate the curved surface area of a cone, we need to find the slant height of the cone first.
The slant height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides. In a cone, the slant height, the height, and the radius form a right-angled triangle.
In this case, the height is 3 cm, and the base diameter is 8 cm. So, the radius (half of the diameter) is 8/2 = 4 cm.
Let's calculate the slant height using the Pythagorean theorem:
Slant height^2 = Radius^2 + Height^2
Slant height^2 = 4^2 + 3^2
Slant height^2 = 16 + 9
Slant height^2 = 25
Taking the square root of both sides, we find:
Slant height = √25
Slant height = 5 cm
Now, we can calculate the curved surface area of the cone using the formula:
Curved Surface Area = π * Radius * Slant height
Curved Surface Area = π * 4 cm * 5 cm
Curved Surface Area = 20π cm^2
Therefore, the curved surface area of the cone is 20π cm^2.
To calculate the curved surface area of a cone, you need to find the slant height of the cone and then use it to calculate the lateral surface area.
Step 1: Find the slant height (l)
The slant height can be found using the Pythagorean theorem, where the height (h) is one leg and half the base diameter (r) is the other leg. The radius (r) can be found by dividing the base diameter by 2.
In this case, the height (h) is 3 cm and the base diameter is 8 cm, so the radius (r) = 8 cm / 2 = 4 cm.
Using the Pythagorean theorem:
l^2 = r^2 + h^2
l^2 = 4^2 + 3^2
l^2 = 16 + 9
l^2 = 25
l = √25
l = 5 cm
Step 2: Calculate the curved surface area (CSA)
The formula for the curved surface area is CSA = πrl, where π (pi) is a mathematical constant approximately equal to 3.14159, r is the radius, and l is the slant height.
In this case, the radius (r) is 4 cm and the slant height (l) is 5 cm.
CSA = π * 4 * 5
CSA = 20π cm²
Therefore, the curved surface area of the cone is 20π cm².