Find the volume, curved surface area and the total surface area of a cone

Question:

Find the volume, curved surface area and the total surface area of a cone whose height and slant height are 6 cm and 10 cm respectively.

Solution:

Height of the cone, h = 6 cm
Slant height of the cone, l = 10 cm

Radius, $r=\sqrt{l^{2}-h^{2}}=\sqrt{100-36}=\sqrt{64}=8 \mathrm{~cm}$

Volume of the cone $=\pi r^{2} h$

$=\frac{1}{3} \times 3.14 \times 8^{2} \times 6$

$=401.92 \mathrm{~cm}^{3}$

Curved surface area of the cone $=\pi r l$

$=3.14 \times 8 \times 10$

$=251.2 \mathrm{~cm}^{2}$

$\therefore$ Total surface area $=\pi r l+\pi r^{2}$

$=251.2+3.14 \times 8^{2}$

$=452.16 \mathrm{~cm}^{2}$

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