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
Ii=9*288=2592
2592/360=7.2cm
9*288 =2592
2592 /360 =7.cm
pi D = 18 pi
so circumference of base circle = (288/360) *18 pi
radius = circumference / 2 pi
= 9 (288/360) = 7.20 cm
To find the radius of the base of the cone, let's calculate the circumference of the circle first. The formula for the circumference of a circle is C = πd, where C represents the circumference and d represents the diameter.
Given that the diameter of the circle is 18 cm, we can substitute this value into the formula to find the circumference:
C = πd
C = π × 18 cm
C = 18π cm
Now, let's calculate the length of the arc that forms the sector of the circle. The formula for the length of an arc is L = (θ/360) × C, where L represents the length of the arc, θ represents the angle in degrees, and C represents the circumference.
In this case, the angle θ is 288 degrees, and the circumference C is 18π cm. Substituting these values into the formula, we have:
L = (288/360) × (18π cm)
L = 0.8 × 18π cm
L = 14.4π cm
The length of the arc represents the circumference of the base of the cone.
Since the base of the cone is a circle, the circumference can be calculated using the formula C = 2πr, where r represents the radius of the base.
Now, we can equate the length of the arc (14.4π cm) to the circumference of the base (2πr cm) of the cone:
14.4π cm = 2πr cm
We can cancel out π on both sides of the equation:
14.4 = 2r
Finally, we solve for r by dividing both sides by 2:
r = 14.4/2
r = 7.2 cm
Therefore, the radius of the base of the cone is 7.2 cm.