Weird math problems??? plz help!?

Question

1) The edge of a cube is 4.50 x 10^-3cm. What is the volume of the cube in cm^3?

2) Calculate the volume of spherical atom of chlorine that has a radius of 1.05 x 10^-10m.

V = 4/3 x II x r^3

3) Calculate the radius of a sphere whose volume is 10.00cm^3.

V= 4/3 x II x r^3

4) Calculate the length of each side of a cube that has a volume of 73.6cm^3.

V= L x W x H

5) Calculate the energy of a particle that has no mass at rest but has mass of 1.3 x 10^-35 kg when it is traveling at the speed of light. Make sure you give units. Use einstein;s formula E= m x c^2 ; c = speed of light = 3.00 x 10^8 m/sec.

1Joule= 1kg x m^2/sec^2

Ok, what the h**l do these problems mean and how do you do them. I don't expect anyone to be able to solve them all but if you can, then, well, ur a freak..

Answer 1

1)

We know the volume of a cube is given by:

V = x³

Where x is the length of the side. Each of your sides are (4.5 * 10^-3) whihc is 4.5/1000.

V = (4.5 / 1000)³

V = (91.12500 / 1,000,000,000)

V = 9.1125 × 10^-8 cm³

Answer 2

1 ) use formula=a^3 for volume of a cube where a=length of edge

{4.5 x10^-3}^3=(4.5)^3 x (10^-3)^3

=91.125 x 10^-9 cc

2 ) volume of sphere=(4/3)*pi*r^3 where r=radius

V= (4/3) x 3.14 x [1.05 x 10^-10 ]^3cubic metre

= 4.187 x (1.05)^3 x (10^-10)^3

=4.187 x 1.1576 x 10^-30

=4.847 x 10^-30 cu.metre

3) here it is (4/3) x 3.13 x (r)^3 cc=10 cc

4.187 x r^3=10

or r^3= 10/4.187=2.388

r= 3rd root of 2.388=1.336 cm  answer

4 )a^3=73.6 cc

or a= 3rd root of 73.6=4.192 cm

5 ) E=mc^2

=1.3 x 10^-35 x3 x 10^8

=3.9 x 10^-27 kg x m/sec^2

=3.9 x 10^-27 Joules

Actually the problem to be solved by simple multiplications.In this age of computer/internet/calculator all the above problems done in 20 secs