Question

A cube of 11 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of base are 15 cm and 12 cm, find the rise in water level in the vessel.

Answer 1

Given: A cube of edge 11 cm is immersed completely in a rectangular vessel of base 15 cm by 12 cm.

Step-wise calculation:

1. Volume of cube

= 11³ 

= 1331 cm³

2. Area of vessel base

= 15 × 12

= 180 cm²

3. Rise in water level

h = `"Volume displaced"/"Base area"` 

= `1331/180` cm 

= `7 + 71/180` cm

1331 ÷ 180 = 7 remainder 71 

⇒ h = `7 71/180` cm

⇒ h = 7.394444... cm 

⇒ h = 7.39 cm (to 2 d.p.).

The water level rises by `1331/180` cm, i.e. `7 71/180` cm ≈ 7.39 cm.