The radius and slant height of a cone are in the ratio of $2:7$. If its curved surface area is $704 \, cm^2$,find its radius $(r)$,slant height $(l)$,and height $(h)$.

(N/A) Let the radius $r = 2x$ and the slant height $l = 7x$.
The curved surface area of a cone is given by $CSA = \pi rl$.
Given $CSA = 704 \, cm^2$ and taking $\pi = \frac{22}{7}$:
$704 = \frac{22}{7} \times (2x) \times (7x)$
$704 = 22 \times 2 \times x^2$
$704 = 44x^2$
$x^2 = \frac{704}{44} = 16$
$x = 4$.
Thus,radius $r = 2 \times 4 = 8 \, cm$ and slant height $l = 7 \times 4 = 28 \, cm$.
The height $h$ is given by $h = \sqrt{l^2 - r^2} = \sqrt{28^2 - 8^2} = \sqrt{(28-8)(28+8)} = \sqrt{20 \times 36} = \sqrt{720} = 12\sqrt{5} \, cm$.