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.
Find the area of the lid fitting to this vessel.
Moreover, find the volume of the water included in this vessel.
Answer
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.
150 cm2
2000 cm3
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.
