An empty cylindrical vase with a radius of 8 cm and a height of 9 cm is filled with 6 cm^3 of sand every 15 seconds. at the same time 8cm^3 of sand is taken out of the vase every minute. after how many minutes will the base be half filled with sand?

General Idea:

The volume of cylinder is given by , where r is the radius and h is the height of the cylinder.

Applying the concept:

Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.

Volume of full cylinder

Volume of half cylinder

Step 2: Let x be the number of minutes of filling the sand.

of sand filled every 15 seconds, there are four 15 seconds in a minute.

So volume of sand filled in 1 minute.

of sand taken out of cylindrical vase every minute.

Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute

Net volume of sand filled in 1 minute

Volume of sand filled in x minutes .

We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.

Conclusion:

The number of minutes required for the base be half filled with sand is 57

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step-by-step explanation:

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