Answer:
a. 5.25cm
b. 374.6 cm^2
Step-by-step explanation:
The radius of the conical cup is half the length of the arc formed
Mathematically, the length of the arc would be;
L = theta/360 * 2 * pi * r
L = 135/360 * 2 * 22/7 * 14 = 33 cm
Now, the arc of this sector will become the base circumference of the circular base of the cone
Thus;
2 * pi * R = 33
2 * 22/7 * R = 33
R = (7 * 33)/44 = 5.25 cm
b. The volume of the cone
Kindly note that the radius of the circle becomes the height of the cone
Mathematically;
V = 1/3 * pi * r^2 * h
Kindly note that the radius of the circle will become the slang height of the cone
We can use pythagoras’ theorem to find the height of the cone
Pythagoras theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides
So here, slant height l is the hypotenuse, h and r are the other two sides
So 14^2 -5.25^2 = h^2
h^2 = 168.4375
h = 12.98 cm
Volume is thus ;
1/3 * pi * 5.25^2 * 12.98 = 374.6 cm^3
