Question

Determine the total surface area of a cone of diameter 6 cm and depth of 5 cm.

• A. $3\sqrt{34}\pi +9\pi {\text{cm}}^2$
• B. $1.5\sqrt{34}\pi +9\pi {\text{cm}}^2$
• C. $6\sqrt{34}\pi +9\pi {\text{cm}}^2$
• D. $3\sqrt{34}\pi {\text{cm}}^2$

Answer 1

The correct option is A $3\sqrt{34}\pi +9\pi {\text{cm}}^2$

Diameter of a cone = d = 6 cm
$\therefore$ Radius of a cone $=\frac{d}{2}$ = 3 cm

Lets draw a cone of given dimensions.
For the cone given in the figure,
Radius $=r=3$ cm and height $=h=5$ cm.
Slant height $=l=\sqrt{r^2+h^2}$
Slant height $=l=\sqrt{3^2+5^2}$
$=\sqrt{9+25}$
$=\sqrt{34}cm$

Curved Surface Area(CSA) $=\pi rl$
Curved Surface Area(CSA) $=\pi \times 3\times \sqrt{34}$
Curved Surface Area(CSA) $=3\sqrt{34}\pi c{m}^2$

Total Surface Area(TSA) $=CSA+\pi r^2$
Total Surface Area(TSA) $=3\sqrt{34}\pi +\pi \left(3^2\right)$
Total Surface Area(TSA) $=3\sqrt{34}\pi +9\pi {\text{cm}}^2$