Math Problem (Level 2) : Suitable lid for vessel (KK1)

A figure is a development view of a vessel without a lid.

Find the area of the lid fitting to this vessel.

Moreover, find the volume of the water included in this vessel.

Answer

150 cm²
2000 cm³

Solution

A sketch is drawn by using the quadrangle ABCD in Fig. 1 as the bottom, it will become as it is shown in Fig. 2. 

The portion of a lid is △EFG in Fig. 2. 

Since FG = CD = 20cm, the area is 15 × 20 / 2 = 150cm². 

As shown in Fig. 3, this solid is made of cutting out the red triangular prism from the quadratic prism. 

The volume of a quadratic prism is (20 + 5) × 20 / 2 × 10 = 2500cm³. 

The volume of a red triangular prism is 5 × 10 / 2 × 20 = 500cm³. 

The volume of this solid is 2500 - 500 = 2000cm³.