Q107 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

The radius of a sphere is 7 cm . If an error of $0.08 \mathrm{sq} . \mathrm{cm}$. is made in measuring it, then the approximate error (in cubic cm ) found in its volume is

  • Correct answer
    A
    0.28
  • B
    0.32
  • C
    0.96
  • D
    0.098

Solution

$r=7 ; A=4 \pi r^2$ $\begin{aligned} & \frac{\mathrm{dA}}{\mathrm{dr}}=8 \pi \mathrm{r} \Rightarrow d A=8 \pi r d r \\ & \Rightarrow \frac{0.08}{8 \pi \mathrm{r}}=\mathrm{dr} \Rightarrow \frac{0.01}{\pi \mathrm{r}}=\mathrm{dr} \\ & \mathrm{V}=\frac{4}{3} \pi \mathrm{r}^3 \Rightarrow \frac{\mathrm{dV}}{\mathrm{dr}}=4 \pi \mathrm{r}^2 \\ & \Rightarrow \mathrm{dV}=4 \pi \mathrm{r}^2 \frac{0.01}{\pi \mathrm{r}} \Rightarrow \mathrm{dV}=4 \times 7 \times 0.01=0.28\end{aligned}$

Hence, the correct answer is option: 'A'.

Relevant Questions