Question

The length of a cuboid is twice its breadth. The breadth is twice its height. Then, find the ratio of the TSA to the square of the height of the cuboid.
[3 Marks]

Answer 1

Let, 'l' be the length, 'b' be the breadth and 'h' be the height of the cuboid.

Given,
length of the cuboid, l =2b,
breadth of the cuboid, b=2h,
Therefore,
l = 2 x 2h = 4h (1 mark)

Total surface area of the cuboid
= 2 (lb + bh +lh)
= 2 (4h x 2h + 2h x h + 4h x h)
= 28 $h^2$ (1 mark)

Therefore, the ratio of the TSA to the square of height can be written as:
$\frac{TSA}{h^2}=\frac{28h^2}{h^2}$
=$\frac{28}{1}$

Therefore, the required ratio is 28:1 (1 mark)