Surface Areas and Volumes — Question 8

Given,

Volume of cone = 9856 cm³

Diameter of the cone (d) = 28 cm

Radius of the cone (r) = $\dfrac{\text{Diameter}}{2} = \dfrac{28}{2}$ = 14 cm.

(i) Let height of cone be h cm.

Volume of the cone = 9856 cm³

Substituting values we get :

$\Rightarrow \dfrac{1}{3}πr^2h = 9856 \\[1em] \Rightarrow h = 9856 \times \dfrac{3}{πr^2} \\[1em] \Rightarrow h = 9856 \times \dfrac{3}{\dfrac{22}{7} \times 14^2} \\[1em] \Rightarrow h = 9856 \times \dfrac{3 \times 7}{22 \times 196} \\[1em] \Rightarrow h = \dfrac{206976}{4312} \\[1em] \Rightarrow h = 48 \text{ cm}.$

Hence, the height of the cone = 48 cm.

(ii) Let slant height of the cone be l cm.

By formula,

$\Rightarrow l = \sqrt{r^2 + h^2} \\[1em] \Rightarrow l = \sqrt{(14)^2 + (48)^2} \\[1em] \Rightarrow l = \sqrt{196 + 2304} \\[1em] \Rightarrow l = \sqrt{2500} = 50 \text{ cm}.$

Hence, the slant height of the cone = 50 cm.

(iii) By formula,

Curved surface area of cone = πrl

Substituting values we get :

⇒ Curved surface area of cone = $\dfrac{22}{7}$ × 14 × 50

= 22 x 2 x 50

= 44 x 50

= 2200 cm².

Hence, curved surface area of cone = 2200 cm².