Question

When a copper sphere is heated, maximum percentage change will be observed in

• A. radius
• B. area
• C. volume
• D. None of these

Answer 1

The correct option is C

volume

Step 1: Given data

Heated copper sphere.

Step 2: To find

We have to determine the maximum percentage change will observe in?

Step 3: Calculation

Change in volume:

$$\begin{gathered} =\frac{∆\left(\frac{4}{3}{\mathrm{\pi r}}^3\right)}{\left(\frac{4}{3}{\mathrm{\pi r}}^3\right)} \\ =\frac{{\mathrm{\Delta r}}^3}{{\mathrm{r}}^3} \\ =\frac{3\mathrm{\Delta r}}{\mathrm{r}} \\ =3\mathrm{X} \end{gathered}$$

Step 4: Change in Radius:

$$\begin{gathered} =\frac{∆\mathrm{r}}{\mathrm{r}} \\ =\mathrm{X} \end{gathered}$$.

Step 5: Change in Area:

$$\begin{gathered} =\frac{∆\left(4{\mathrm{\pi r}}^2\right)}{4{\mathrm{\pi r}}^2} \\ =\frac{∆{\mathrm{r}}^2}{{\mathrm{r}}^2} \\ =\frac{2∆\mathrm{r}}{\mathrm{r}} \\ =2\mathrm{X} \end{gathered}$$

Three times the radius change in percentage. As a result, the volume shows the greatest percentage change.

Therefore the correct option is C.