The length and breadth of a cuboid are $30\, cm$ and $25\, cm$. If the total surface area of the cuboid is double the lateral surface area of the cuboid,find its height and volume.

(N/A) Let the length $l = 30\, cm$,breadth $b = 25\, cm$,and height be $h\, cm$.
The lateral surface area $(LSA)$ of a cuboid is given by $2h(l + b) = 2h(30 + 25) = 110h\, cm^2$.
The total surface area $(TSA)$ of a cuboid is given by $2(lb + bh + lh) = 2(30 \times 25 + 25h + 30h) = 2(750 + 55h) = 1500 + 110h\, cm^2$.
According to the problem,$TSA = 2 \times LSA$.
$1500 + 110h = 2(110h)$.
$1500 + 110h = 220h$.
$110h = 1500$.
$h = \frac{1500}{110} = \frac{150}{11}\, cm$.
The volume $V = l \times b \times h = 30 \times 25 \times \frac{150}{11} = 750 \times \frac{150}{11} = \frac{112500}{11}\, cm^3$.