Question

http://puu.sh/fiy3n.png

Answer 1

Since the sun is so far away, you can approximate the rays of light hitting the earth as parallel. The Sun is 9 degrees south of vertical in Alexandria. If you draw radii from the center of the earth to each city, the angle formed is 9 degrees also, from opposite interior angles.

9 degrees of arc is given as 400 km in the problem. We will assume the earth is a perfect sphere. 9 degrees goes into 360 degrees exactly 40 times. \[40~*~9^{\circ} = 40~*~400~km\]\[360^{\circ} = 16000~km\]

Using the data, the circumference of the earth in this problem is 16000 km.

Answer 2

Thanks, I figured out the first one earlier from dividing 360/9 to get 40 then just multiplied it by 400 km.

The other two though I am still stuck.

Answer 3

Radius of Sphere = 2.8 cm
Mass of Sphere = 0.06 kg

Density in [kg / m^3]

Answer 4

\[Volume = \frac{ 4 }{ 3 }\pi*r^3\]
\[Density = \frac{ Mass }{ Volume }\]

Answer 5

You want the density to be in units kg per cubic meter. I would convert the radius to meters first before calculating the volume of the sphere.

radius = 2.8 cm = 0.028 m

\[Volume = \frac{ 4 }{ 3 }\pi*r^3 = \frac{ 4 }{ 3 }\pi*(0.028 ~m)^3\]

Answer 6

The volume turns out to be, \[V \approx 9.2*10^{-5}~~ m^3\]

Answer 7

Therefore the density is,
\[\rho = \frac{ 0.06~kg }{ 9.2*10^{-5}~m^3 } \approx 652.5~~\frac{ kg }{ m^3 }\]

Answer 8

The second Sphere has radius = 4.5 cm = 0.045 m and the same density.

The mass of the second Sphere will be :\[mass =density*volume \]

Answer 9

Thank you, the formulas are very helpful