how to find the curved surface area of a cone when the height is 25mm and circumference is 132mm ?
a = πrs
where
2πr = 132
s^2 = r^2+h^2
To find the curved surface area of a cone, you need to know the slant height or the slant angle. However, in this case, you have been given the height of the cone and the circumference of the base. Using this information, we can calculate the slant height first and then find the curved surface area.
Step 1: Calculate the radius of the base
The circumference of a circle (base of the cone) is given by the formula C = 2πr, where C is the circumference and r is the radius of the base.
132mm = 2πr
Divide both sides by 2π:
r = 132mm / (2π) = 21mm (rounded to the nearest whole number)
Step 2: Calculate the slant height
The slant height, denoted as "l," can be found using the Pythagorean theorem. It is the hypotenuse of a right triangle formed by the height of the cone and the radius of the base. Let h be the height of the cone, r be the radius of the base, and l be the slant height.
Using the Pythagorean theorem: h^2 + r^2 = l^2
Plugging in the values: 25^2 + 21^2 = l^2
625 + 441 = l^2
l^2 = 1066
l ≈ √1066 ≈ 32.68mm (rounded to two decimal places)
Step 3: Calculate the curved surface area
The curved surface area (CSA) of a cone is given by the formula CSA = πrl, where r is the radius of the base and l is the slant height.
CSA = π * 21mm * 32.68mm ≈ 2167.63mm² (rounded to two decimal places)
Therefore, the curved surface area of the cone is approximately 2167.63mm².
To find the curved surface area of a cone, you need to know the slant height of the cone. However, in this case, you are given the height of the cone and the circumference of its base. So, we first need to find the slant height.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 132 mm, so we can set up the equation as follows:
132 = 2πr
To find the radius, we can rearrange the equation as follows:
r = 132 / (2π)
Next, we can find the slant height using the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle formed by the height (h) and the radius (r). The formula is given as:
l = √(r^2 + h^2)
Now, substitute the values of r and h into the equation:
l = √((132 / (2π))^2 + 25^2)
After calculating the value of l, you can use it to find the curved surface area (A) using the formula:
A = πrl
Substitute the values of r and l into the equation:
A = π * (132 / (2π)) * l
After simplifying, you will have the answer, which will give you the curved surface area of the cone.