Question

The volume of a cone is 9856 cu cm. If the diameter of its base is 28 cm, what is its height and slant height?

Answer 1

Diameter of cone (d) = 28 cm
Radius of cone (r) =Diameter ÷ 2=28 ÷ 2=14 cm
Height of cone (h) = ?
Volume of cone = 9856 cu cm
Volume of a cone =$\frac{1}{3}\mathrm{\pi }{r}^{2}h$
$$\begin{gathered} \Rightarrow 9856=\frac{1}{3}\times \frac{22}{7}\times 14\times 14\times h \\ \Rightarrow h=\frac{9856\times 3\times 7}{22\times 14\times 14} \\ \Rightarrow h=48 \end{gathered}$$
The height and radius of a cone form a right angle.
Suppose the slant height is l cm.
By Pythagoras Theorem,
l² = r² + h²
⇒ l² = 14² + 48²
⇒ l² = 196 + 2304
⇒ l² = 2500
⇒ l = 50