Question

The ratio of the total surface area and the lateral surface area of a right cone is 4 : 3 and its height is 8 m, then its base area is approx

• A. $24m^2$
• B. $33m^2$
• C. $21m^2$
• D. $27m^2$

Answer 1

Answer: (A)

$24m^2$

Total
surface area of a cone $=\pi r(r+l)$ where r is the radius of the
cone and l is the slant height.

Curved
surface area of a cone $=\pi rl$ where r is the radius of the cone and
l is the slant height.
Given, $ \frac {
\pi r (r + l) }{\pi rl} = \frac {4}{3} => \frac { r + l }{l} = \frac {4}{3} => 3r + 3l = 4l l = 3r $

For a cone, l $=\sqrt{h^2+r^2}$ where h is the height.

Hence, $3r=\sqrt{8^2+r^2}$

$=>9r^2=64+r^2$

$ 8 {r}^{2} = 64 {r}^{2} = 8 $Areaofthebase$ = \pi{r}^{2} = \frac {22}{7} \times 8 = 25.15 {cm}^{2} $