The height and slant height of a cone are measured as 15cms and 25cms. Errors $2\%$ are to allowed in both of these lengths. The possible error in its volume is

$In a cone height of the cone, radius of the base and slant height of the cone form a right angled triangle$

$$\begin{gathered} r^2=l^2-h^2 \\ {25}^2-{15}^2 \\ 400 \\ also 2r\delta r=2l\delta l -2h\delta h \end{gathered}$$

$\begin{array}{l}h=15\mathrm{cm},\delta h=\frac{2h}{100};l=25\mathrm{cm}\Rightarrow \delta l=\frac{2l}{100},r=20\\ r\delta r=\frac{l^2}{50}-\frac{h^2}{50}=\frac{400}{50}=8\\ \therefore \delta r=\frac{8}{r}=\frac{8}{20}=\frac{2}{5}\\ \Rightarrow v=\frac{1}{3}\pi r^{2}h,\delta v=\frac{\pi }{3}\left(r^2\delta h+h.2r\delta r\right)\\ =\frac{\pi }{3}\left(400·\frac{15}{50}+2·15·20·\frac{2}{5}\right)\\ =\frac{\pi }{3}\left(120+240\right)\\ =120\pi \\ \text{ Hence option (D) is correct. }\end{array}$