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

1. How much water was there in Tank K at first?
2. Vaidev then poured all the water from Tank L into Tank K. 6000 cm³ of water overflowed from Tank K. What was the height of Tank K?

(a)
Volume of water to fill Tank L
= 20 x 18 x 20
= 7200 cm<sup>3

1</sup>₃ of volume of water in Tank K at first = 7200 cm^3  
3₃ of volume of water in Tank K at first = 3 x 7200 = 21600 cm³

Volume of water in Tank K at first = 21600 cm³

Volume of water in Tank L at first
= 20 x 18 x 22
= 7920 cm³

Total volume of water in Tank K and Tank L 
= 21600 + 7920
= 29520 cm³

Final volume of water in Tank K after 6000 cm³ of water overflowed
= 29520 - 6000
= 23520 cm³

Base area of Tank K
= 24 x 20
= 480 cm²

Height of Tank K
= 23520 ÷ 480 
= 49 cm

Answer(s): (a) 21600 cm² ; (b) 49 cm