Question

A cone of height $8m$ has a curved surface area $188.4m^2$. The radius of the base is:
(Take $\pi =3.14$):

• A. $4m$
• B. $4.5m$
• C. $5m$
• D. $6m$

Answer 1

The correct option is D $6m$

Height of the cone is not given
Assuming height of the cone $=8m$

Let radius of base of cone $=r$

Curved surface area of cone $=188.4c{m}^2$

$\pi rl=188.4c{m}^{2}l=\sqrt{r^2+h^2}=\sqrt{r^2+8^2}=3.14\times r\times \sqrt{r^2+64}=188.4=r\sqrt{r^2+64}=60$

Squaring both sides, we get

$r^2(r^2+64)=3600r^4+64r^2-3600=0r^4+100r^2-36r^2-3600=0(r^2+100)(r^2-36)=0r^2-36=0r^2=36r=6m$