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Question:

Note Use $\pi=\frac{22}{7}$, 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.

Solution:

Radius of the cone, r = 35 cm

Height of the cone, h = 12 cm

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

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

(ii) Curved surface area of the cone $=\pi r l=\frac{22}{7} \times 35 \times 37=4070 \mathrm{~cm}^{2}$

(iii) Total surface area of the cone $=\pi r(r+l)=\frac{22}{7} \times 35 \times(35+37)=\frac{22}{7} \times 35 \times 72=7920 \mathrm{~cm}^{2}$

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