Hong Kong F.3 Maths Questions (URGENT)?

Question

Excuse me. I am doing corrections for my maths homework book but I am puzzled with question below. Can anyone teach me how to do so?
1. May cuts a semi circle of diameter 20cm from a piece of paper, and forms a right circular cone. Find a. the base radius of the cone and b. the volume of the cone.

Answer 1

The base of the cone will be formed by the outside arc of the semi-circle. That is, the circumference of the base of the cone will be half the circumference of the circle of diameter 20 cm. Thus the circumference of the bottom of the cone is 10 cm*pi. The corresponding radius satisfies:

2*pi*r = 10cm*pi

so r = 5 cm. Now the volume of a cone with height h and base radius r is

V = 1/3 pi h r^2.

So you just need to figure out the height. If you look at a cross section of the cone you will see a right triangle with hypotenuse 10 cm, and base 5 cm. Thus the height is sqrt(75). Therefore the volume is

1/3 pi sqrt(75) 25.

Answer 2

Since the 1/2 diameter of 20cm will be the perimeter of the circular base of the cone you have 20 = 2pix R where R is the base radius of the cone.

Knowing R lets you calculate the volume = 1/3 H pi R^2
The height of the cone is H = sqrt(r^2 -R^2) where r is the radius of the original semi circle (r = 20/2 = 10 cm)

Answer 3

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Answer 4

the circumfrence of a circle is 2piD, since May only used 1/2 we see the base of the cone has circumfrence of piD that would be 20pi cm. that is just the set up
a) we want r but what we have are values of D
we now have a circle of curcumfrence 20pi cm and circumfrence is 2piD=20pi
that means D=10 cm
r=D/2=10/2= 5cm

b) use the volume of a cone formula