1) The Moon is approximately a sphere of radius 1.74 106 m. (a) What is its circ

Question

1)

The Moon is approximately a sphere of radius 1.74 106 m.

(a) What is its circumference in kilometers?

________. km

(b) What is its surface area in square kilometers?

_________ km2

(c) What is its volume in cubic kilometers?

_________km3

2)

Antarctica is roughly semicircular, with a radius of about r = 1950 km (see figure below). The average thickness of its ice cover is h = 3100 m. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of Earth.)
______________ cm3

3)

Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber.

(a) If a sample of gold, with a mass of 66.31 g, is ressed into a leaf of 6.000 m thickness, what is the area of the leaf?
____________ m2

(b) If, instead, the gold is drawn out into a cylindrical fiber of radius 3.900 m, what is the length of the fiber?
____________ km

Explanation / Answer

[1] ans

Given that

radius r=1.74*10^6 m

the circumference of the sphere =2*3.14*r=2*3.14*1.74*10^6 =10.9272*10^3 km

the surface of the sphere =4*3.14*r^2=4*3.14*(1.74*10^6)^2=38*10^6 km^2

the volume of the sphere =4/3*3.14*(1.74*10^6)^3=22.1*10^9 km^3

......................................................................................................................................................

2 ans

Given that

radius r=1950 km

thickness h=3100 m=3.1 km

now we find the volume of the antarctica

area A=3.14*1950^2/2=5969925 km^2

volume V=5969925*3.1=18506767.5 km^3=1.851*10^16 cm^3

..............................................................................................................................................................

............................................................................................................................................................

3 ans

Given that

density d=19.32*10^3 kg/m^3

[a] ans

mass m=66.31*10^-3 kg

thickness t=6*10^-6 m

now we find the area of the leaf

volume=mass/density=66.31*10^-3/19.32*10^3

=3.4322*10^-6 m^3

area a=volume/thickness=3.4322*10^-6/6*10^-6=0.572 m^2

[b] ans

radius of the cylinder r=3.9*10^-6 m

area A=3.14*(3.9*10^-6)^2=47.8*10^-12 m^2

now we find the thickness

volume=area*length

3.4322*10^-6=47.8*10^-12*Length

length L=0.072*10^6=72 km

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