Question

Note Use $\mathrm{\pi }=\frac{22}{7}$, unless stated otherwise.
Find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height is 12 cm.

Answer 1

Radius of the cone, r = 35 cm

Height of the cone, h = 12 cm

∴ Slant height of the cone, $l=\sqrt{r^2+h^2}=\sqrt{{35}^2+{12}^2}=\sqrt{1225+144}=\sqrt{1369}$ = 37 cm

(i) Volume of the cone = $\frac{1}{3}\mathrm{\pi }{r}^{2}h=\frac{1}{3}\times \frac{22}{7}\times {\left(35\right)}^2\times 12$ = 15400 cm³

(ii) Curved surface area of the cone = $\mathrm{\pi }rl=\frac{22}{7}\times 35\times 37$ = 4070 cm²

(iii) Total surface area of the cone = $\mathrm{\pi }r\left(r+l\right)=\frac{22}{7}\times 35\times \left(35+37\right)=\frac{22}{7}\times 35\times 72$ = 7920 cm²