A sector if circle substends at an angle 270 degree. With a radius of 14cm. It is folded into a cone,
a] what is the base radius of the cone
b] what is the total surface area of the cone?
(a) r = 270/360 * 14
(b) a = πr(r+14)
73.5
To find the answers, we need to understand a few formulas and concepts related to circles and cones.
a] To find the base radius of the cone, we can use the formula for the circumference of a circle and the angle subtended by the sector:
Circumference of a circle = 2πr (where r is the radius of the circle)
Angle subtended by a sector = θ degrees (in this case, θ = 270 degrees)
Since the angle of the sector is 270 degrees, it means that the sector covers 270/360 = 3/4th of the entire circle.
So, the sector is 3/4th of the circumference of the circle. Therefore, we can set up the equation:
Sector length = (3/4) * 2πr
In this case, the sector length is equal to the circumference of the cone's base. So, we have:
2πr = (3/4) * 2πr
Simplifying the equation, we find:
r = (3/4) * r
Cancelling r from both sides, we get:
1 = 3/4
This is not possible, so there must be an error in the given information. Please recheck the angle subtended by the sector.
b] To find the total surface area of the cone, we need to consider two parts: the curved surface area and the base area of the cone.
The curved surface area of a cone is given by the formula:
Curved Surface Area = πrl
where r is the base radius of the cone and l is the slant height of the cone.
The slant height of the cone can be found using the Pythagorean theorem:
l^2 = r^2 + h^2
where h is the height of the cone.
Since the cone is formed by folding the sector into a cone, the height of the cone is the radius of the sector, h = 14 cm.
Using this information, we can find the base radius of the cone and then use it to calculate the total surface area. However, since there seems to be an error in the given information, we cannot find the exact values for the base radius and the total surface area at this time.
Please provide the correct angle subtended by the sector, and we can proceed with the calculations.