Question

12. A piece of paper is in the shape of a sector of a circle whose radius is 12 cm and the central angle of
the sector is 120°. It is rolled to form a cone of the biggest possible capacity. Find the capacity of the
cone.​

Answer 1

Answer:

area of sector =x°/360°×πr²

=120°/360°×22/7×12×12

3×144×3.14

=1356.48 cm²

Step-by-step explanation:

I know in this way

Answer 2

Answer:

When the sector is cut from the circle it will have a curved length of one third of the circle. This will be πd/3 where d is the 24 cm diameter of the circle. This yields:

π(24)/3 = 8π

When the cone is rolled it will then have a circular base with this 8π circumference. The cone will also have a side length of 12 cm, which is important to find the height of the cone. First we need to find the radius of the base of the cone. We know that the circular base has a circumference of 8π and :

c=πd So we get:

8π=πd

d=8 and r=4 <--- Radius of the circular base.

For the height use the Pythagorean theorem:

r^2+(height)^2=(side )^2

4^2+(height)^2=12^2

h^2=144-16

h^2=128

h=8√2

Thus the formula for the volume of a cone:

V=1/3bh Where b is the area of the base.

V=1/3π(4)^2(8√2)

V=1/3π128√2 <----- Answer

V=189.56 <----- Approximate answer

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