The slant height of a cone is $25 \,cm$ and its curved surface area is $550 \,cm^{2}$. Find the radius,height,and the total surface area of the cone.

(N/A) Given: Slant height $(l) = 25 \,cm$,Curved Surface Area $(CSA) = 550 \,cm^{2}$.
$1$. Finding the radius $(r)$:
$CSA = \pi r l$
$550 = \frac{22}{7} \times r \times 25$
$r = \frac{550 \times 7}{22 \times 25} = 7 \,cm$.
$2$. Finding the height $(h)$:
Using the relation $l^{2} = h^{2} + r^{2}$:
$25^{2} = h^{2} + 7^{2}$
$625 = h^{2} + 49$
$h^{2} = 625 - 49 = 576$
$h = \sqrt{576} = 24 \,cm$.
$3$. Finding the total surface area $(TSA)$:
$TSA = \pi r(l + r)$
$TSA = \frac{22}{7} \times 7 \times (25 + 7)$
$TSA = 22 \times 32 = 704 \,cm^{2}$.