The circumference of base of a right circular cone is 88 cm. if the height of the cone is 28 cm, then what is the curved surface area of the cone

To find the curved surface area of the cone, we need to first calculate the slant height of the cone.

The circumference of the base of the cone is given as 88 cm. We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.

Since the base of the cone is a circle, we can find the radius by dividing the circumference by 2π.

Radius (r) = Circumference / (2π) = 88 cm / (2π)

Next, we need to find the slant height (l) of the cone. The slant height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (l) is equal to the sum of the squares of the other two sides (r and h).

Using the given height of the cone (h = 28 cm) and the radius we calculated earlier, we can find the slant height.

l^2 = r^2 + h^2

l^2 = (88 cm / (2π))^2 + (28 cm)^2

Now, we can calculate the slant height (l) by taking the square root of both sides of the equation.

l = √[(88 cm / (2π))^2 + (28 cm)^2]

Once we have the slant height, we can calculate the curved surface area (CSA) of the cone using the formula CSA = πrl, where r is the radius and l is the slant height.

CSA = π * (88 cm / (2π)) * l

Finally, we can substitute the value of l that we calculated earlier to find the curved surface area of the cone.