Chapter 18, Problem 45A

a.

To determine

Volume of the gold cube.

Answer to Problem 45A

Volume of cube, $V=0.027{\text{ m}}^3$

Explanation of Solution

Given:

Side of the metal cube, $a=0.30\text{ m}$

Formula used:

Volume of the cube is given by, $V=a^3$

Where, V is volume and a is side of cube.

Calculation:

Now, substituting the value of a and solve.

  $\begin{array}{c}V={\left(0.30\right)}^3\\ =0.027{\text{ m}}^3\end{array}$

Conclusion:

Therefore, volume of the cube is, $V=0.027{\text{ m}}^3$ .

b.

To determine

Mass of the cube.

Answer to Problem 45A

Mass of cube, $m=521.1\text{ kg}$

Explanation of Solution

Given:

Density of the cube, $d=1.93\times {10}^4{\text{ kg/m}}^3$

Formula used:

  $m=dV$

Where, m is mass, d is density and V is volume.

Calculation:

From part (a) $V=0.027{\text{ m}}^3$

Now, substituting the value of d and V and solve.

  $\begin{array}{l}m=1.93\times {10}^4\times 0.027\\ =521.1\text{ kg}\end{array}$

Conclusion:

Therefore, mass of the cube is 521.1 kg.

c.

To determine

Weight of the cube in Newton and in pound.

To identify: Whether the cube can be lift or not.

Answer to Problem 45A

Weight of cube is 5106.78 N and in pound 1123.49 lb as weight is very large so it is not possible to lift it.

Explanation of Solution

Given:

Side of the metal cube, $a=0.30\text{ m}$

Density of the cube, $d=1.93\times {10}^4{\text{ kg/m}}^3$

  $1\text{N}=\text{0}\text{.22 lb}$

Formula used:

  $W=mg$

Where, W is weight, m is mass and gis acceleration due to gravity.

Calculation:

From part (b) $m=521.1\text{ kg}$

Acceleration due to gravity, $g=9.8{\text{ m/s}}^2$

Now, substituting the value of m and g and solve.

  $\begin{array}{l}W=521.1\times 9.8\\ =5106.78\text{ N}\end{array}$

Now, in pound weight will be,

  $\begin{array}{l}5106.78\text{ N = 0}\text{.22}\times \text{5106}\text{.78 lb}\\ \text{=1123}\text{.49 lb}\end{array}$

As weight is very large so it is not possible to lift it.

Conclusion:

Therefore, weight of cube is 5106.78 N and in pound 1123.49 lb as weight is very large so it is not possible to lift it.