Question

answer the questions below. give exact integer or decimal answers. be sure to include the correct units in your answers. (a) an object has a density of 18 \\(\frac{\text{kg}}{\text{m}^3}\\) and a mass of 720 kg. what is the volume of the object? volume = \\(\square\\) (b) another object has a volume of 112 \\(\text{m}^3\\) and a mass of 896 kg. what is the density of the object? density = \\(\square\\)

Explanation:

Part (a)

Step1: Recall density formula

The formula for density is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. We need to solve for $V$, so rearrange the formula to $V=\frac{m}{
ho}$.

Step2: Substitute values

Given $
ho = 18\frac{\text{kg}}{\text{m}^3}$ and $m = 720\text{ kg}$. Substitute into the formula: $V=\frac{720\text{ kg}}{18\frac{\text{kg}}{\text{m}^3}}$.

Step3: Simplify the expression

When dividing by a fraction, we multiply by its reciprocal. So $\frac{720}{18}=40$, and the units $\text{kg}$ cancels out, leaving $\text{m}^3$. So $V = 40\text{ m}^3$.

Part (b)

Step1: Recall density formula

Again, use $
ho=\frac{m}{V}$, where $m = 896\text{ kg}$ and $V = 112\text{ m}^3$.

Step2: Substitute values

Substitute into the formula: $
ho=\frac{896\text{ kg}}{112\text{ m}^3}$.

Step3: Simplify the expression

Divide $896$ by $112$: $\frac{896}{112} = 8$. So $
ho = 8\frac{\text{kg}}{\text{m}^3}$.

Answer:

(a) $40$ cubic meters
(b) $8$ kilograms per cubic meter