Question

Mark (✓) against the correct answer in each of the following:
The height of a cone of diameter 10 cm and slant height 13 cm is
(a) 12 cm
(b) 13 cm
(c) $\sqrt{69}\mathrm{cm}$
(d) $\sqrt{194}\mathrm{cm}$

Answer 1

(a) 12 cm

$$\begin{gathered} \mathrm{Radius}=\frac{\mathrm{Diameter}}{2}=\frac{10}{2}=5\mathrm{cm} \\ \mathrm{We}\mathrm{know}\mathrm{that} \\ {l}^2=h^2+r^2 \\ \Rightarrow h=\sqrt{l^2-r^2} \\ =\sqrt{{13}^2-5^2} \\ =\sqrt{169-25} \\ =\sqrt{144} \\ =12\mathrm{cm} \end{gathered}$$