Question

A sector of a circle of radius 12cm has the angle 120o. It is rolled up so that two bounding radii are joined to form a cone. Find the volume of the cone.

Answer 1

Answer:

Step-by-step explanation:

Your 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

Answer 2

The require answer is  362 $\sqrt{132}$/21.

Given the radius of circle 12cm

This becomes the slant height of cone

The angle of sector 120°.

The length of arc is given as = $\frac{x}{360}$ x 2πr

                                                = $\frac{120}{360}$ x 2 x π x 12

                                                 = $\frac{1}{3}$ x 2 x π x 12

                                                 = 4 x 2 x π

                                                  = 8π

This become the circumference of base circle= 2πr =8π

2r = 8

r =4

According to Pytagorous theorm

(Slantheight)^2 = (hight)^2 + (radius)^2

$(12)^{2}$ =  (hight)^2 + $4^{2}$

(hight)^2  = 144 -16

                = 132

hight = $\sqrt{132}$

Volume of cone = $\frac{1}{3}$ π$r^{2}$h

                            = $\frac{1}{3}$ x π x 4 x4 x $\sqrt{132}$

                             =   $\frac{1}{3}$ x$\frac{22}{7}$ x 4 x4 x $\sqrt{132}$

                              = 362 $\sqrt{132}$/21

Hence the require answer is  362 $\sqrt{132}$/21.

To learn more geometry follow the given link

https://brainly.com/question/22051318?

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