KK.24 Four solids in water tank

In the water tank of the rectangular prism of Fig. 1, four solids as shown in Fig. 2 are placed for the shadow face to be as the bottom.

Then, water is poured into this water tank every 10 cm3/s.

(1) When the depth of water is to be 2 cm, find the area of the water surface.

(2) After (1), find the time when it will take until the water fills up the tank.

The volume of the solid of Fig. 2 can be calculated as (base area) × (height) × 1/3.

Answer

(1) 103.5 cm²
(2) 78.3 seconds

Reference