A cone is formed by bending a sector of a circle having an angle of 288 degrees.find the radius of the base of the cone if the diameter of the circle is 18cm
the radius of the circle is 9.
since s = rθ, the arc length of the base of the cone is
s = 9 * 288/360 * 2π
so, the radius of the base of the cone is s/2π = 9 * 288/360
Find the surface area of a cone made by bending a sector of radius 25cm and cetral angle 288°
To find the radius of the base of the cone, we need to determine the radius of the circle.
We know that the diameter of the circle is 18 cm. The diameter is twice the radius, so the radius of the circle is (18 cm) / 2 = 9 cm.
Now we can find the circumference of the circle using the formula C = π * d, where C represents the circumference and d represents the diameter.
C = π * 18 cm
C = 18π cm
Next, we will calculate the length of the arc that forms the cone. The angle of the sector is given as 288 degrees, which is more than a full circle (360 degrees). We need to convert this angle to radians by multiplying by (π/180).
Angle in radians = (288 degrees) * (π/180) = 8π/5 radians
The length of the arc is given by the formula Arc Length = (Angle in radians) * (Radius).
Arc Length = (8π/5) * (9 cm)
Now, since the circumference of the circle is equal to the length of the arc, we can equate the two:
18π cm = (8π/5) * (9 cm)
Simplifying the equation, we can cancel out the π on both sides:
18 = (8/5) * 9
Next, we'll solve for the unknown radius by isolating it on one side of the equation:
r = (8/5) * 9 / 18
Now, simplify the expression:
r = (8/5) * 1/2
r = 8/10
r = 0.8 cm
Therefore, the radius of the base of the cone is 0.8 cm.