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# The volume of a right circular cone is 9856 $${cm}^3$$ . If the diameter of the base is 28 cm, findi) height of the coneii) slant height of the coneiii) curved surface area of the cone.

Given :
Radius of the base = $$\frac{28}{2} cm = 14 cm$$
Also, Volume of a right circular cone = 9856 $${cm}^3$$

i) Let the height of the cone be h.

But, we know that,

Volume of right circular cone = $$\frac{1}{3} {\pi} {r}^2 h$$
$$\Rightarrow$$ 9856 $${cm}^3$$ = $$\frac{1}{3} × \frac{22}{7} × {14}^2 × h$$ $${cm}^2$$
$$\Rightarrow$$ h = 48 cm.

Therefore, height of the cone is 48 cm.

ii)We know, slant height of cone
= $$\sqrt({h}^2 + {r}^2)$$ cm
= $$\sqrt({48}^2 + {14}^2)$$ cm
l = $$50 cm$$

Therefore, slant height of the cone is 50 cm.

iii) We also know that,
Curved surface area of the cone
= $${\pi}rl$$
= $$\frac{22}{7} × 14 × 50 {cm}^2$$
= 2200 $${cm}^2$$

Therefore, the curved surface area of the cone is 2200 $${cm}^2$$.