Question

For a right circular cone with radius $=r$, height $=h$ and slant height $=l$, which of the following is not true?

• A. Always $l>h$
• B. Always $i>r$
• C. Always $r>\pi$
• D. $l^2=r^2+h^2$

Answer 1

Answer: (A)

Always $l>h$

In a right circular cone, height $\left(h\right)$, radius $\left(r\right)$ and slant height $\left(l\right)$ are always the sides of right triangle, because the height of the cone is always perpendicular to its radius. Then, the height, radius and slant height of the cone make a right angled triangle, in which,

$(\text{Slant height}{)}^2=(\text{Radius}{)}^2+(\text{Height}{)}^2$

$⟹l^2=r^2+h^2$.

Since slant height $l$ represents hypotenuse, so it is always larger then other sides,

$\therefore l>h$ is false.
Hence, option $A$ is correct.