Question

Determine the curved surface area of a cone of diameter 12 cm and depth of 8 cm.

• A. $60\pi c{m}^2$
• B. $50\pi c{m}^2$
• C. $40\pi c{m}^2$
• D. $30\pi c{m}^2$

Answer 1

The correct option is D $30\pi c{m}^2$

Diameter of a cone = d = 12 cm
$\therefore$ Radius of a cone $=\frac{d}{2}$ = 6 cm

Lets draw a cone of given dimensions.
For the cone given in the figure,
Radius $=r=6$ cm and height $=h=8$ cm.
Slant height $=l=\sqrt{r^2+h^2}$
Slant height $=l=\sqrt{6^2+8^2}$
$=\sqrt{36+64}$
$=\sqrt{100}$
$=\sqrt{10\times 10}$
$=10cm$

Curved Surface Area(CSA) $=\pi rl$
Curved Surface Area(CSA) $=\pi \times 6\times 10(\because r=6cm;l=10cm)$
Curved Surface Area(CSA) $=60\pi c{m}^2$