The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone
(Assume π = 22/7)
Volume of a right circular cone = 9856 cm3
Diameter of the base = 28 cm
(i) Radius of cone, r = \(\frac{28}{2}\) cm = 14 cm
Let the height of the cone be h
Volume of cone, V = \(\frac{1}{3}\) πr2h
\(\frac{1}{3}\) πr2h = 9856
\(\frac{1}{3}\) × \(\frac{22}{7}\) × 14 × 14 × h = 9856
h = 48
The height of the cone is 48 cm.
(ii) Slant height of cone, l = \(\sqrt{r^2 + h^2}\)
l = \(\sqrt{14^2 + 48^2}\)
= \(\sqrt{196 + 2304}\)
= 50
Slant height of the cone is 50 cm.
(iii) curved surface area of cone = πrl
= \(\frac{22}{7}\) × 14 × 50
= 2200
curved surface area of the cone is 2200 cm2.