ABC26GN5002 · Volume and Surface Area

Let the correct radius be 100 cm. Then, measured radius = 101.5 cm. $$\begin{aligned} & \begin{aligned} \therefore \text { Error in volume } & =\frac{4}{3} \pi\left[(101.5)^{3}-(100)^{3}\right] \mathrm{cm}^{3} \\ & =\frac{4}{3} \pi(1045678.375-1000000) \mathrm{cm}^{3} \\ & =\left(\frac{4}{3} \times \pi \times 45678.375\right) \mathrm{cm}^{3} . \end{aligned} \\ & \begin{aligned} \therefore \text { Error } \%=\left\{\frac{\frac{4}{3} \pi(45678.375)}{\frac{4}{3} \pi(100 \times 100 \times 100)} \times 100\right\} \% & =4.56 \% \\ & =4.6 \%(\mathrm{app} .) . \end{aligned} \end{aligned}$$