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

1. How much water was there in Tank R at first?
2. Liam then poured all the water from Tank S into Tank R. 2016 cm³ of water overflowed from Tank R. What was the height of Tank R?

(a)
Volume of water to fill Tank S
= 16 x 14 x 14
= 3136 cm<sup>3

1</sup>₃ of volume of water in Tank R at first = 3136 cm^3  
3₃ of volume of water in Tank R at first = 3 x 3136 = 9408 cm³

Volume of water in Tank R at first = 9408 cm³

Volume of water in Tank S at first
= 16 x 14 x 17
= 3808 cm³

Total volume of water in Tank R and Tank S 
= 9408 + 3808
= 13216 cm³

Final volume of water in Tank R after 2016 cm³ of water overflowed
= 13216 - 2016
= 11200 cm³

Base area of Tank R
= 20 x 16
= 320 cm²

Height of Tank R
= 11200 ÷ 320 
= 35 cm

Answer(s): (a) 9408 cm² ; (b) 35 cm