Question

For the question given below, four alternative choices have been provided of which only one is correct. You have to select the correct choice:

The diameter and height of a right circular cone are 7 cm and 12 cm, respectively. The volume of the cone (in cm³) is:

(a) 88

(b) 112

(c) 154

(d) 616

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cone},r=\frac{7}{2}=3.5\mathrm{cm}\mathrm{and} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cone},h=12\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ =\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 12 \\ =\frac{22}{21}\times 147 \\ =22\times 7 \\ =154{\mathrm{cm}}^3 \end{gathered}$$

Hence, the correct choice is option (c).