Hello, and also welcome come this video about cylinders! In this video, we will check out how to discover the volume and also surface area of any type of cylinder. Stop learn about cylinders!

Cylinders are among the most typical three-dimensional forms that us see about us. Many food and also drink cans room shaped like a cylinder. Another quite typical item that we see daily that is shaped choose a cylinder is a battery. Take it a look about you, can you see any cylindrical shapes?

As you can see, all these objects have a circular top and bottom and a curved surface. A cylinder is a three-dimensional figure with two circular bases that are parallel to every other and are join by a curved surface. The perpendicular street that connects the bases the the cylinder is the height and also the axis is the line that extends through the centers the the circular bases.

A cylinder where the axis is perpendicular come the bases is called a right cylinder. A cylinder wherein the axis is no perpendicular to the bases is called an oblique cylinder.

Let us recall what volume and surface area that three-dimensional figures are and how us go about finding them.

You are watching: Volume of a right circular cylinder

The volume of a three-dimensional figure is the quantity of fluid it deserve to hold, and it is measured in cubic units.

The surface area of a three-dimensional figure is the total area the the surface of the number covers and is measured in square units.

The formula because that the volume (V) and also surface area (SA) of a cylinder space shown. To calculate the volume and also surface area of any type of cylinder, we require the radius and the elevation of the cylinder. The formula for the area the a one is $$A=\pi r^2$$

It is no surprised that the formula appears in both the volume and surface area formulas because that a cylinder due to the fact that the bases of a cylinder room circles.

Very lot like other three-dimensional figures, the volume the a cylinder is the area that its circular basic multiplied by the height.

$$V=\pi r^2h$$ $$SA=2\pi rh+2\pi r^2$$
$$r$$ = radius that the base $$h$$ = elevation of cylinder

The surface area, as we mentioned before, is the complete area that covers the surface of the figure. This can be much easier to watch if we open the cylinder up and also look at its net. The area the the two circular bases is the $$2\pi r^2$$ component of the surface ar area formula. When the cylinder is open, we can see the curved part of the cylinder is yes, really a rectangle and the side lengths of the rectangle are identified by the circumference of the circular basic $$2\pi r$$ and also the height of the cylinder $$h$$.

Let’s look at an example:

What is the volume and also surface area the a cylinder where the diameter the the basic is 18mm and the height of the cylinder is 20mm? (Leave her answer in terms of $$\pi$$)

So, to find the volume and surface area, we need the radius and the elevation of the cylinder. Because the radius is fifty percent of the diameter, we can just division 18 by 2, therefore the radius of the circular basic is just 9 millimeters. Currently we have the right to substitute the values into the formula and also evaluate.

$$V=\pi r^2h=\pi (9\text mm)^2(20\text mm)=1,620\pi \text mm^3$$ $$SA=2\pi rh+2\pi r^2=2\pi (9)(20)+2\pi (9)^2=360\pi +162\pi =522\pi \text mm^2$$

Let’s look at at one more example.

The surface area that a cylinder is 502.4 ft² and also the radius that the basic is 5 ft. What is the height of the cylinder? (Use 3.14 for $$\pi$$)

We will begin by substituting the worths we know right into the surface ar area formula.

As you deserve to see there is just one unknown, $$h$$, so us will use our algebra skills to fix for the unknown.

simplify every term

$$502.4=2(3.14)(5)h+2(3.14)(5)^2$$

isolate the term through the variable

$$502.4=31.4h+157$$

combine choose terms

$$502.4-157=31.4h+157-157$$

solve for h

$$345.4=31.4h$$

divide both political parties by the coefficient to isolation the variable

$$\frac345.431.4=\frac31.431.4h$$

Therefore, the height of the cylinder is 11 ft.

$$11=h$$

Joan has a water tank at her shop the is 34.8 customs high and also the diameter that the circular basic is 20.6 inches. She desires to obtain a label created the side of the tank with her company logo and needs to calculation the lateral area, which is the surface area without the area the the bases. What is the area of the label? (Use 3.14 for $$\pi$$)

since we only need the lateral area, we deserve to remove the area that the circles from ours formula.

$$\textlateral area (LA)=2\pi rh$$

Remember, the formula asks because that the radius the the base, therefore we will certainly divide 20.6 by 2 to acquire 10.3, i m sorry is the length of the radius.

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$$LA=2\pi rh=2(3.14)(10.3)(34.8)=2,251 \text in^2$$

So the area the our label will have to be $$2,251\text in^2$$.

I hope the this video clip on volume and also surface area that a cylinder to be helpful! thanks for watching, and also happy studying!