You already found that CD = 6cm. There is a faster way to calculate the cross section area.

Area of cross section

= Area of a rectangle AFGH - area of a rectangle BCDE

= GH × AH - BE × BC

= 10m × 8m - 6m × 4.5m

= 80m² - 27m²

= 53m²


Volume of tank = area of cross section × width

= 53m² × 3m

= 159m³

how about (b)

How do I find the water level if 125m3 is poured inside?

The water will fill beyond the level where CD is.

So calculate the volume up to CD first.

Height from GH to CD = 8m - 4.5m = 3.5m

Volume of water that will occupy the container up to the level where CD is

= 10m × 3.5m × 3m
= 105m³

Volume of the water that fills the remaining part of the tank

= 125m³ - 105m³
= 20m³

Now look at the remaining two identical sections.

Each has a base area of :

2m × 3m = 6m²
Combined base = 6m³ × 2 = 12m²

Height that they will be filled to

= 20 m³ ÷ 12m²
= 1⅔m


So, height of water in the tank

= 3.5m + 1⅔m
= 5 1/6 m
= 5.1666... m
= 5.2m (1d.p)

The water will fill beyond the level where CD is.

So calculate the volume up to CD first.

Height from GH to CD = 8m - 4.5m = 3.5m

Volume of water that will occupy the container up to the level where CD is

= 10m × 3.5m × 3m
= 105m³

Volume of the water that fills the remaining part of the tank

= 125m³ - 105m³
= 20m³

Now look at the remaining two identical sections.

Each has a base area of :

2m × 3m = 6m²
Combined base = 6m³ × 2 = 12m²

Height that they will be filled to

= 20 m³ ÷ 12m²
= 1⅔m


So, height of water in the tank

= 3.5m + 1⅔m
= 5 1/6 m
= 5.1666... m
= 5.2m (1d.p)