A right open top cylinder with a capacity of 0.5 liters, need measurement facts

Question

A right open top cylinder, with a capacity of 0.5 liters, the radius is 4cm. What is the surface area? 

Answer 1

We have an open top cylinder, therefore the surface area will be made up of the area of the bottom circle plus the area of the rest of the cylinder. You can call this the lateral surface or the part you put your hand around to hold the cylinder, like a can of soda.

If you took away the bottom circle you would have a cylinder without a top or a bottom. An example of this would be what is left of a roll of paper towels if you used up all the paper towels, the piece of cylindrical cardboard. If you made a vertical cut the entire length of the cylinder and flattened this out you would have a rectangle whose length would be the circumference of the cylinder and whose width would be the height of the cylinder. Now we can find the surface area.

A liter is a cubic decimeter; all edges measure 1 decimeter which is 1/10 of a meter. Instead of 1 decimeter for the measures of the edges we will use 10 centimeters because the radius is 4 centimeters.

The volume of a liter is 10*10*10=1000 cubic cm. Your cylinder has a volume of 0.5 L, or 500 cubic cm.

The next step is to find the height(h) of the cylinder.

The formula for the volume of a cylinder is V=pi*r^2*h

500=3.14159*4^2*h

500=3.14159*16*h

500=50.2654*h

500/50.2654=h

h=9.9472 cm

The area of the bottom circle plus the area of the lateral surface will give us the total surface area.

The area of a circle is given by the formula A=pi*r^2

A=3.14159*4^2

A=3.14159*16

A=50.2654 sq cm

The area of the lateral surface, which will be a rectangle when we cut the cylinder and flatten it out, is given by the formula A=l*w where the length is the circumference of the cylinder and the width is the height of the cylinder.

The circumference is given by the formula C=2*pi*r.

C=2*3.14159*4

C=3.14159*8

C=25.1327 cm

We know that the width is the height which we found to be 9.9472 cm.

The area of the rectangle is l*w or C*h which is:

A=25.1327*9.9472

A=249.9999 sq cm

Now add the two areas together: 249.9999+50.2654=300.26539 sq cm

The surface area of the open top cylinder is 300.26539 square centimeters