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.