# Units of measurement

1) A sphere has a radius 1.500m Find its volume in cm^3. Find its suface area in m^2 and in mm^2?

2) A truncated right circular cone has dimensions:

upper base diameter =1.50cm

lower base diameter = 4.00cm

height = 6.00cm

Find its volume in cm^3, m^3, mm^3

3) a person walks 5km in 1,5hr. What is the speed in mi/hr, m/s, and ft/s?

4) A car can accelerate from rest to 60 mi/hr in 7 s. Express this acceleration in the following units(assume constant acceleration)

ft/s^2

km/hr/s

m/s^2

5)A turntable accelerates from rest to 33 rpm in 0.6s. Express this acceleration in rev/s^2 and rad/s^2.

6)A spbway train starts from rest at a station, accelerates uniformly at a rate of 2.0 m/s^2 for 15 s, cruises at constant speed fro 30 s, and then decelerates uniformly coming to rest at the next station after a total trip time of 54 s. How far apart are the stations? Express your answers in m, km and miles.

7)An electrically powered grindstone wheel rotates at 2,000 rpm for 50 s and the power is then switched off. The wheel comes to rest 40.0 s later. Calculate: The angular deceleration in rad/s ^2 and rev/min/s.

Determine the total angular distance traveled over the 90 s time interval, expressed in both radians and revolutions?

#### Solution Preview

1) A sphere has a radius 1.500m Find its volume in cm^3. Find its surface area in m^2 and in mm^2?

r= 1.5 metres

= 150 cm

= 1500 mm

Volume=(4/3)pi r 3= 14137167 cm3

Surface area=4pi r 2= 28.2743 m2

= 28274333.88 mm2

2) A truncated right circular cone has dimensions:

upper base diameter =1.50cm

lower base diameter = 4.00cm

height = 6.00cm

Find its volume in cm^3, m^3, mm^3

To find the volume of the truncated cone

Volume=(1/3)pi r1 2 (h1+h2)-(1/3)pi r2 2 h2=

r1= lower base radius 2 cm

or 0.02 m

or 20 mm

r2= upper base radius 0.75 cm

or 0.0075 m

or 7.5 mm

h1= height of truncated cone 6 cm

or 0.06 m

or 60 mm

h2= height by which the cone has been truncated

h2/(h1+h2)=r2/r1

or h2/(6+h2)=0.75/2= 0.375

or h2= 3.6 cm

or 0.036 m

or 36 mm

Putting these values into the equation

Volume= 38.09181092 cm3

0.000038092 m3

38091.81 mm2

Velocity-acceleration

3) a person walks 5km in 1.5hr. What is the speed in mi/hr, m/s, and ft/s?

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#### Solution Summary

Expresses physical quantities in different units of measurement are examined. A truncated right circular cone has dimensions are provided.