Question

A solid cylinder $r=17.5cm$ , $h=16.5cm$ has a mass of $13.49kg$ . This cylinder is floating in water. Then oil is poured on top of the water until the situation. How much of the height of the cylinder is in the oil?

Answer 1

 

 

 

To determine how much of the height of the cylinder is in the oil, you need to calculate the volume of the cylinder and the volume of the oil that is needed to completely submerge the cylinder.

First, calculate the volume of the cylinder using the formula

$V=\pi r^{2}h$

where V is the volume, r is the radius of the cylinder, and h is the height of the cylinder. In this case, the radius of the cylinder is 17.5 cm and the height is 16.5 cm, so the volume of the cylinder is:

$V=\pi \left(17.5cm{)}^2\right(16.5cm)V=87,695.625c{m}^3$

Next, you need to determine the density of the oil. Let's assume that the density of the oil is 0.8 g/cm^3. You can then calculate the volume of the oil that is needed to completely submerge the cylinder by dividing the mass of the cylinder by the density of the oil:

$V=\frac{m}{Density}V=\frac{13.49kg}{0.8g/c{m}^3}V=16,862.5c{m}^3$

 

Finally, divide the volume of the oil by the volume of the cylinder and multiply by the height of the cylinder to determine how much of the height of the cylinder is in the oil:

$H_{oil}=\left(\frac{V_{oil}}{V_{cylinder}}\right)\times h{H}_{oil}=\left(\frac{16,862.5c{m}^3}{87,695.625c{m}^3}\right)\times 16.5cm{H}_{oil}=8.42cm$

 

So, approximately 8.42 cm of the height of the cylinder is in the oil.

So, approximately 8.42 cm of the height of the cylinder is in the oil.