Mensuration - Units of Measure

Calculate the area of a rectangle with length $0.8\text{ m}$ and width $45\text{ cm}$ in $\text{cm}^2$.

First, convert the length to centimeters: $0.8\text{ m} = 0.8 \times 100 = 80\text{ cm}$ Now calculate the area: $A = \text{length} \times \text{width}$ $A = 80\text{ cm} \times 45\text{ cm}$ $A = 3600\text{ cm}^2$

Before performing calculations, ensure all units are consistent. Here, meters were converted to centimeters before multiplying.

A water tank has a volume of $2.5\text{ m}^3$. How many liters of water does it hold?

Convert cubic meters to cubic centimeters: $2.5\text{ m}^3 = 2.5 \times (100)^3\text{ cm}^3$ $2.5\text{ m}^3 = 2.5 \times 1,000,000 = 2,500,000\text{ cm}^3$ Since $1000\text{ cm}^3 = 1\text{ litre}$: $\text{Capacity} = \frac{2,500,000}{1000} = 2500\text{ litres}$

We first use the volume conversion factor $(100)^3$ to find $cm^3$, then divide by $1000$ to convert to liters.

Convert a speed of $108\text{ km/h}$ to $\text{m/s}$.

Convert kilometers to meters: $108\text{ km} = 108 \times 1000 = 108,000\text{ m}$ Convert hours to seconds: $1\text{ hour} = 60 \times 60 = 3600\text{ seconds}$ Calculate speed: $\text{Speed} = \frac{108,000\text{ m}}{3600\text{ s}} = 30\text{ m/s}$

Compound units are converted by changing the numerator and denominator separately.

Find the total mass in grams of three items weighing $1.5\text{ kg}$, $450\text{ g}$, and $0.75\text{ kg}$.

Convert all masses to grams: $1.5\text{ kg} = 1500\text{ g}$ $0.75\text{ kg} = 750\text{ g}$ Add the values: $\begin{array}{r} 1500 \\ 450 \\ + 750 \\ \hline 2700 \end{array}$ Total mass = $2700\text{ g}$

Convert kilograms to grams by multiplying by $1000$ and then sum the values.

$\text{Area in m}^2 = 4\text{ m} \times 3\text{ m} = 12\text{ m}^2$ $\text{Conversion factor: } 1\text{ m}^2 = 10,000\text{ cm}^2$ $\text{Area in cm}^2 = 12 \times 10,000 = 120,000\text{ cm}^2$

First, calculate the area in square meters. Since $1\text{ m} = 100\text{ cm}$, the area conversion factor is $100^2 = 10,000$. Multiply the area in $\text{m}^2$ by $10,000$ to get the result in $\text{cm}^2$.

$\text{Volume} = 5\text{ cm} \times 5\text{ cm} \times 5\text{ cm} = 125\text{ cm}^3$ $\text{Mass} = \text{Density} \times \text{Volume}$ $\text{Mass} = 8\text{ g/cm}^3 \times 125\text{ cm}^3 = 1000\text{ g}$ $\text{Mass in kg} = \frac{1000}{1000} = 1\text{ kg}$

First, find the volume of the cube using $V = s^3$. Then, use the density formula rearranged for mass ($M = D \times V$). Finally, convert the mass from grams to kilograms by dividing by $1000$.