A sector of a circle radius 18 cm and angle 300 degrees is bent to form a cone. Calculate the base radius of the cone
the radius of the base is ... 18 cm * (300º / 360º)
To find the base radius of the cone formed, we need to find the circumference of the sector and equate it to the circumference of the base of the cone.
The circumference of a sector of a circle can be calculated using the formula:
Circumference = (θ/360) * 2 * π * r
where θ is the angle in degrees, r is the radius, and π is approximately 3.14159.
In this case, the angle given is 300 degrees and the radius is given as 18 cm. So, we can substitute these values into the formula to find the circumference of the sector:
Circumference = (300/360) * 2 * 3.14159 * 18 cm
= (5/6) * 2 * 3.14159 * 18 cm
= 30 * 3.14159 cm
≈ 94.2478 cm
Since the circumference of the sector is equal to the circumference of the base of the cone, we can equate it to the formula for the circumference of a circle:
Circumference = 2 * π * cone_base_radius
By rearranging the formula, we can solve for the cone_base_radius:
cone_base_radius = Circumference / (2 * π)
= 94.2478 cm / (2 * 3.14159)
≈ 15 cm
Therefore, the base radius of the cone is approximately 15 cm.