There is an water tank shaped as a rectangular prism as shown in Fig.1 and the height of the surface of the water is 16 cm.
Answer
(1) 6696 cm3
There is a container shaped as a rectangular prism of 20 cm in depth as shown in Fig.2.
The work with which water is drawn out of an water tank as much as possible using this container was done continuously twice.
Answer the following questions.
Noted that a triangle with which the ratio of length of three sides is 3 : 4 : 5 is the triangle with which the angle facing the longest side is 90 degrees.
(1) Find the volume of the water which remaining in the water tank after drawn out for the 1st time.
(2) Find the volume of the water drawn out for the 2nd time.
Answer
(1) 6696 cm3
(2) 1728 cm3
Solution
(1) In the case of the Fig.3 below, the container can contain water most.
Solution
(1) In the case of the Fig.3 below, the container can contain water most.
△ ABE and△ AFD are homothetic in Fig.4.
The volume of the water drawn out is (20 + 11) × 12 × 1/2 × 12 = 2232 cm3.
(2) The height of the remaining water in an water tank is 6696 / (18 × 31) = 12 cm.
In the case of the Fig.5 below, the container can contain water most.
The volume of the water drawn out at the 2nd time is (20 + 4) × 12 × 1/2 × 12 = 1728 cm3.
