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10) A cylindrical can of internal radius 20 cm stand upright on a flat surface. It contains water to a

depth of 20 cm. Calculate the rise in the level of the water when a brick of volume 1500 cm³ is
immersed in the water.

1 Answer

6 votes

Answer:

To calculate the rise in the water level when a brick of volume 1500 cm³ is immersed in the water in the cylindrical can, you can use the formula for the volume of a cylinder:

Volume = πr²h

Where:

- Volume is the volume of the cylinder (in this case, the volume of water)

- π is approximately 3.14159

- r is the radius of the cylinder

- h is the height of the water level in the cylinder

Initially, the can contains water to a depth of 20 cm, and its internal radius is 20 cm. So, the initial volume of water is:

Initial Volume = π(20 cm)²(20 cm) = 8000π cm³

Now, when the brick with a volume of 1500 cm³ is immersed in the water, the total volume of water and the brick combined will be:

Total Volume = Initial Volume (water) + Volume of Brick

Total Volume = 8000π cm³ + 1500 cm³

Now, you can calculate the new height of the water level (h') using the formula:

Total Volume = π(20 cm)²(h')

8000π cm³ + 1500 cm³ = π(20 cm)²(h')

Now, solve for h':

h' = (8000π cm³ + 1500 cm³) / (π(20 cm)²)

h' ≈ (8000π + 1500) / (π(400)) cm ≈ (8000π + 1500) / 1256 cm ≈ 8.01 cm (rounded to two decimal places)

So, the rise in the water level when the brick is immersed in the water is approximately 8.01 cm.

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