The figure shows the amount of water in two rectangular tanks, Y and Z, at first. Andy poured ¹₃ of the water from Y into Z to fill it to the top, without overflowing.

1. How much water was there in Tank Y at first?
2. Andy then poured all the water from Tank Z into Tank Y. 2470 cm³ of water overflowed from Tank Y. What was the height of Tank Y?

(a)
Volume of water to fill Tank Z
= 19 x 17 x 18
= 5814 cm<sup>3

1</sup>₃ of volume of water in Tank Y at first = 5814 cm^3  
3₃ of volume of water in Tank Y at first = 3 x 5814 = 17442 cm³

Volume of water in Tank Y at first = 17442 cm³

Volume of water in Tank Z at first
= 19 x 17 x 20
= 6460 cm³

Total volume of water in Tank Y and Tank Z 
= 17442 + 6460
= 23902 cm³

Final volume of water in Tank Y after 2470 cm³ of water overflowed
= 23902 - 2470
= 21432 cm³

Base area of Tank Y
= 24 x 19
= 456 cm²

Height of Tank Y
= 21432 ÷ 456 
= 47 cm

Answer(s): (a) 17442 cm² ; (b) 47 cm