Chapter 18, Problem 43A

(a)

To determine

The volume of the sphere.

Answer to Problem 43A

The volume of the sphere is $33.5{\text{cm}}^3$ .

Explanation of Solution

Given:

The radius of the solid sphere is $r=2.0\text{ cm}$ .

The mass of the solid sphere is $m=352.0\text{ g}$

Formula used:

The expression for volume is,

  $V=\frac{4}{3}\pi r^3$

Here, $r$ is the radius.

Calculation:

The volume of the solid sphere is,

  $\begin{array}{l}V=\frac{4}{3}\pi r^3\\ V=\frac{4}{3}\pi {\left(2.0\text{cm}\right)}^3\\ V=33.5{\text{ cm}}^3\end{array}$

Conclusion:

Thus, the volume of the sphere is $33.5{\text{cm}}^3$ .

(b)

To determine

The surface area of the sphere.

Answer to Problem 43A

The surface area of the sphere is $50.0{\text{cm}}^2$ .

Explanation of Solution

Given:

The radius of the solid sphere is $r=2.0\text{ cm}$ .

The mass of the solid sphere is $m=352.0\text{ g}$

Formula used:

The expression for surface area is,

  $A=4\pi r^2$

Here, $r$ is the radius.

Calculation:

The surface area of the solid sphere is,

  $\begin{array}{l}A=4\pi r^2\\ A=4\pi {\left(2.0\text{cm}\right)}^2\\ A=50.0{\text{ cm}}^2\end{array}$

Conclusion:

Thus, the surface area of the sphere is $50.0{\text{cm}}^2$ .

(c)

To determine

The density of the sphere.

Answer to Problem 43A

The density of the sphere is $10.5\text{g}/{\text{cm}}^{\text{3}}$ .

Explanation of Solution

Given:

The radius of the solid sphere is $r=2.0\text{ cm}$ .

The mass of the solid sphere is $m=352.0\text{ g}$

Formula used:

The expression for density is,

  $\rho =\frac{m}{V}$

Here, $m$ is the mass and $V$ is the volume.

Calculation:

From part (a), the volume of the sphere is $V=33.5{\text{cm}}^3$ .

The density of the solid sphere is,

  $\begin{array}{l}\rho =\frac{m}{V}\\ \rho =\frac{352\text{ g}}{33.5{\text{ cm}}^3}\\ \rho =10.5\text{g}/{\text{cm}}^{\text{3}}\end{array}$

Conclusion:

Thus, the density of the sphere is $10.5\text{g}/{\text{cm}}^{\text{3}}$ .

(d)

To determine

The material used to make the sphere and the cube.

Answer to Problem 43A

The cube and sphere are made up of silver.

Explanation of Solution

Given info:

The radius of the solid sphere is $r=2.0\text{ cm}$ .

The mass of the solid sphere is $m=352.0\text{ g}$

Formula used:

The expression for density is,

  $\rho =\frac{m}{V}$

Here, $m$ is the mass and $V$ is the volume.

Calculation:

From part (c), the density of the sphere is $\rho =10.5\text{g}/{\text{cm}}^{\text{3}}$ .

The density of cube is $\rho =10.5\text{g}/{\text{cm}}^{\text{3}}$ .

The material that is reference to the density of $\rho =10.5\text{g}/{\text{cm}}^{\text{3}}$ as silver.

Hence, the cube and sphere are made up of silver.

Conclusion:

Thus, the cube and sphere are made up of silver.