A sink hole on the ground created by the collapse of an old underground mine measures 43.5 m × 37.9 m × 9.6 m. How much volume of earth (soil and rocks) is needed to fill the sink hole? Express your answers in cubic meters and in the correct number of significant figures.

One sphere has a radius of 4.52 cm; another has a radius of 4.72 cm. What is the difference in volume (in cubic centimeters) between the two spheres? Give the answer to the correct number of significant figures. The volume of a sphere is  , where   = 3.1416 and r is the radius.

With a wooden ruler you measure the length of a rectangular piece of sheet metal to be 13 mm m m . You use micrometer calipers to measure the width of the rectangle and obtain the value 5.98 mm m m . Give your answers to the following questions to the correct number of significant figures.

Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μs . They are produced when cosmic rays bombard the upper atmosphere about 11.4 km above the earth's surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth's surface.

What is the greatest distance a muon could travel during its 2.2 μs lifetime?

According to your answer in part A, it would seem that muons could never make it to the ground. But the 2.2 μs lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999 c, what is the mean lifetime of a muon as measured by an observer at rest on the earth?

Express your answer using two significant figures.

How far would the muon travel in this time?

Express your answer using two significant figures.

From the point of view of the muon, it still lives for only 2.2 μs , so how does it make it to the ground? What is the thickness of the 11.4 km of the atmosphere through which the muon must travel, as measured by the muon?

Express your answer using two significant figures.