Find the volume of this cylinder?

Question

This cylinder is floating in water, its length is 6.75m. Its diameter is .45m. .11m of the cylinder is above the surface of the water.

I need to know how to figure out the volume of the submerged portion of this cylinder.

Thank you!

Answer 1

V=6.75*pi*(d/2)^2

x^2=0.11*(0.45-0.11)

a=2*arctg[x/(0.45-0.11)]

S(submerge)=pi*R^2-(a/2*pi)*pi*R^2+x(R...

Vs=V*(S(submerge)/pi*R^2)

Answer 2

The radius od the cylinder is:

r = 0.45/2 = 0.225m, Thus the equation of the cross-section of the cylinder is:

X^2 + Y^2 = (0.225)^2

The height of the water above the center of the circle is;

Y = r - 0.11 = 0.225 - 0.11 = 0.115m, therefore;

X = (0.225^2 - 0.115^2)^0.5 = 0.1934m

The angle of the segment of the cicle above the water is;

A = 2arctan(0.1934/0.115) = 118.5267 degrees

The area under water therefore is:

A = (360-118.5267)/360)(pi x r^2) + XY

A = (241.4733/360)pi (0.225^2) + 0.115 x 0.1934

A = 0.12892m^2

The volume of the cylinder underwater is;

V =A x L = 0.12892 x 6.75 = 0.8702 m^3

Answer 3

The area of the unsubmerged section is a circular segment.

To find the area of the segment we use the formula

A= 0.5r^2 *(theta - sin(theta)),  from reference webpage

theta (in radians) = 2*ACOS(1-2*(depth of unsubmerged section /D)

theta = 2* ACOS (1-2*(0.11/0.45)

theta = 0.512

A = .45^2/8 *(0.512 - sin(0.512))

A = 0.126m

A*L = V of unsubmerged section

0.126m * 6.75m = V of unsubmerged section

0.851m^2 = V of unsubmerged section