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

1. How much water was there in Tank S at first?
2. Riordan then poured all the water from Tank T into Tank S. 2560 cm³ of water overflowed from Tank S. What was the height of Tank S?

(a)
Volume of water to fill Tank T
= 20 x 16 x 16
= 5120 cm<sup>3

1</sup>₃ of volume of water in Tank S at first = 5120 cm^3  
3₃ of volume of water in Tank S at first = 3 x 5120 = 15360 cm³

Volume of water in Tank S at first = 15360 cm³

Volume of water in Tank T at first
= 20 x 16 x 20
= 6400 cm³

Total volume of water in Tank S and Tank T 
= 15360 + 6400
= 21760 cm³

Final volume of water in Tank S after 2560 cm³ of water overflowed
= 21760 - 2560
= 19200 cm³

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

Height of Tank S
= 19200 ÷ 480 
= 40 cm

Answer(s): (a) 15360 cm² ; (b) 40 cm