**1.**An automobile company displays a die-cast model of its first car, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in solid gold from the original dies. What mass of gold is needed to make the new model?

**2.**A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 10

^{-27}kg. Determine the density of the proton

**3.**Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five

times greater. Find its radius.

**4.**What mass of a material with density r is required to make a hollow spherical shell having inner radius

*r*1 and outer radius

*r*

_{2}?

**5.**On an interstate highway in a rural region of Gujarat, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit of 75.0 Km/h?

**6.**Estimate the number of breaths taken during an average human lifetime.

**7.**What if the average lifetime were estimated as 80 years instead of 70? Would that change our final estimate?

**8.**A carpet is to be installed in a rectangular room whose length is measured to be 12.71 m and whose width is measured to be 3.46 m. Find the area of the room.

**9.**The mass of a copper atom is 1.06 10

^{-25 }kg, and the density of copper is 8 920 kg/m

^{3}. (a) Determine the number of atoms in 1 cm

^{3}of copper. (b) Visualize the one cubic centimeter as formed by stacking up identical cubes, with one copper atom at the center of each. Determine the volume of each cube. (c) Find the edge dimension of each cube, which represents an estimate for the spacing between atoms.