The density of aluminium is 2700 \text{kg}/\text{m}^3 /
Given that 1 kg = 2.2 lb and 1 m = 39.4 in, what is the density in \text{lb}/\text{in}^3 ?
We have:
1 kg = 2.2lb
And:
1 m = 39.4 in
We can write:
2\ 700 \dfrac{\text{km}}{\text{m}^3} = 2\ 700 \times \dfrac{2.2\,\text{lb}}{\left(39.4\,\text{in}\right)^3}
= \dfrac{2\ 700 \times2.2}{\left(39.4\right)^3}\dfrac{\text{lb}}{\text{in}^3} = 0.097 \,{\text{lb}}/{\text{inch}}^3
The density of aluminium is 0.097 \,{\text{lb}}/{\text{inch}}^3.
Paul is in a car that is going at a speed of 90 kilometers per hour.
Given that 1 km = 1000 m, what is his speed in meters per second ?
We have:
1 km = 1000 m
And:
1h = 3600 s
We can write:
90 \dfrac{\text{km}}{\text{h}} = 90 \times \dfrac{1\ 000\,\text{m}}{3\ 600\,\text{s}} = \dfrac{90\ 000}{3\ 600}\dfrac{\text{m}}{\text{s}} =25\dfrac{\text{m}}{\text{s}}
Paul is going at a speed of 25 m/s.
Acceleration of gravity is 9.8 \text{m}/\text{s}^2.
Given that 1 \text{ m}= 3{,}28 \text{ ft}, what is the acceleration in feet per square second ?
We have:
1 m = 3.28 ft
We can write:
9.8 \dfrac{\text{m}}{\text{s}^2} = 9.8 \times \dfrac{3.28\,\text{ft}}{\,\text{s}^2} =32.144\dfrac{\text{ft}}{\text{s}^2}
The acceleration of gravity is 32.144\dfrac{\text{ft}}{\text{s}^2} .
The area of a square is 10 \, \text{ft}^2. Given that 1ft= 30.48 cm, what is the area in centimeters squared?
We have:
1 ft = 30.48 cm
We can write:
10 \,\text{ft}^2 = 10 \times \left(30.48\,\text{cm}\right)^2 =10 \times 929.304\,\text{cm}^2= 9\ 290.304\,\text{cm}^2
The area of the square is 9\ 290.304\, \text{cm}^2
The volume of a container is 12 \, \text{cm}^3. Given that 1 cm= 0.4 in, what is the area in inches squared?
We have:
1 cm = 0.4 in
We can write:
12\,\text{cm}^3 = 12 \times \left(0.4 \, \text{in}\right)^3 =12 \times 0.064 \, \text{in}^3=0.768 \, \text{in}^3
The volume of the container is 0.768 \, \text{in}^3.
The area of a garden is 1\, \text{mi}^2.
Given that 1 mi = 1609 m and 1 ha = 10 000 \text{m}^2, what is the area of the garden in hectare?
We have:
1 mi = 1061 m
We can write:
1 \,\text{mi}^2 = \left(1\ 609\,\text{m}\right)^2 = 2\ 588\ 881\,\text{m}^2
Since:
1 \text{ ha}=10\,000\text{ m}^2
We have:
2\ 588\ 881\,\text{m}^2 = \dfrac{2\ 588\ 881}{10\ 000}=258.89
The area of the garden is 258.89 ha.
A train goes at a speed of 360 miles per hour.
Given that 1 mi = 1760 yd, what is the speed in yard per second ?
We have:
1\text{ mi} = 1\ 760\text{ yd}
And:
1\text{ h} = 3\ 600\text{ s}
We can write:
360 \dfrac{\text{mi}}{\text{h}} = 360\times \dfrac{1\ 760\,\text{yd}}{3\ 600\,\text{s}} =176 \text{ yd}/\text{s}
The speed of the train is 176 \text{ yd}/\text{s}.