Understanding Volume and Function in a Glass Tank

The video tutorial explains how to calculate the volume of water needed to fill a glass tank with marbles. It introduces a formula where the water volume, W, is a function of the number of marbles, n, given by W = 32 - 0.05n. The tutorial demonstrates how to determine the tank's total volume by setting n to zero, resulting in 32 liters. It further explains that each marble displaces 0.05 liters of water, thus reducing the water needed by that amount per marble. The video provides a clear understanding of the relationship between the number of marbles and the water volume required.

What does Andrei plan to do with the glass tank?

• Use it as a fish tank

• Fill it with sand

• Use it for storing grains

• Fill it with marbles and water

What is the formula for the volume of water needed in the tank?

• W = 32 - 0.05n

• W = 0.05n - 32

• W = 32n - 0.05

• W = 32 + 0.05n

How can we determine the total volume of the glass tank?

• By measuring the tank directly

• By counting the number of marbles

• By calculating W when n is zero

• By using a different formula

What is the total volume of the glass tank?

• 64 liters

• 0.05 liters

• 32 liters

• 16 liters

What does the term 0.05n in the formula represent?

• The width of the tank

• The weight of the marbles

• The volume of each marble

• The height of the tank

How much less water is needed for each marble added?

• 0.1 liters

• 1 liter

• 0.5 liters

• 0.05 liters

What is the volume of each marble?

• 0.05 liters

• 0.1 liters

• 1 liter

• 0.5 liters

If one marble is added, how much water is needed?

• 31 liters

• 32.05 liters

• 31.95 liters

• 32 liters

Why does adding a marble reduce the water needed by 0.05 liters?

• Because the marble displaces 0.05 liters of water

• Because the marble absorbs water

• Because the marble is large

• Because the marble is heavy

What happens to the water volume when no marbles are in the tank?

• It equals the tank's total volume

• It becomes zero

• It halves

• It doubles