Question

In a swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water by a man is 8 cubic metres, what will be rise in water level?

Answer 1

Given;

Length of swimming pool= 90m=l

Breadth of swimming pool= 40m=b

Displacement of water by 1 man = 8 cu.m.

To find;

Increase in height when 150 men take a dip in the pool (h)

Solution;

• According to Archimedes principle,
• Displacement of liquid = Total volume of body immersed in liquid.
• Displacement of liquid = Increase in volume = l × b × h = 40*90*h
• Volume of immersed body = Volume of 1 man * No. of men= 8*150

• ∴ 40 * 90 * h = 8 * 150
• 3600 * h = 1200
• h = 1200/3600 = 1/3
• h = 0.333 m.

Answer;

The rise in water level will be by 0.333 m.

Answer 2

Given:

Swimming Pool with dimension 90 m by 40 m

150 men took a dip.

Average displacement of water by a man is 8 m³

To Find:

The Rise in water level

Solution:

Find the base area of the swimming pool:

Base area = Length x Breath

Base area = 90 x 40

Base area = 3600 m²

Find the total displacement of water for 150 men:

1 man =  8 m³

150 men = 8 x 150

150 men = 1200 m³

Find the rise in water:

Rise in water = Volume ÷ Base Area

Rise in water = 1200 ÷ 3600

Rise in water = 1/3 m

Answer: The water will rise by 1/3 m