Set up cuboid dimensions

Let the length $l=9x$, breadth $b=5x$, and height $h=2x$. Given the volumes are equal, set $V_{cuboid} = 11250$.

$9x \times 5x \times 2x = 11250$

Solve for x

Simplify the volume equation to solve for $x$. We have $90x^3 = 11250$, so $x^3 = \frac{11250}{90} = 125$.

$x = \sqrt[3]{125} = 5$

Calculate cuboid dimensions

Using $x=5$, find the dimensions: $l = 9 \times 5 = 45$ cm, $b = 5 \times 5 = 25$ cm, and $h = 2 \times 5 = 10$ cm.

$l=45, b=25, h=10$

Calculate Total Surface Area (TSA)

Apply the total surface area formula $TSA = 2(lb + bh + lh)$. Substituting the values: $2(45 \times 25 + 25 \times 10 + 45 \times 10)$.

$TSA = 2(1125 + 250 + 450) = 2(1825) = 3650$