Math - How to find the surface area of a cylinder

The base of a cylinder has an area of $9\pi$ and the cylinder has a height of . What is the surface area of this cylinder?

$90\pi$

$18\pi$

$72\pi$

Explanation

The standard equation for the surface area of a cylinder is

$SA=2\pi r^2+2\pi rh$

where denotes radius and denotes height. We've been given the height in the question, so all we're missing is the radius. However, we are able to find the radius from the area of the circle:

$Area=\pi r^2$

We know the area is $9\pi$

$9\pi =\pi r^2$ so

Now that we have both and , we can plug them into the standard equation for the surface area of a cylinder:

$SA=2\pi (3)^2+2\pi (3)(12)=18\pi +72\pi =90\pi$

What is the surface area of cylinder with a radius of 3 and height of 7?

$51\pi$

$21\pi$

$63\pi$

$10\pi$

Explanation

The surface area of a cylinder can be determined by the following equation:

$SA=2\pi rh+\pi r^2$

$SA=(2\pi)(3)(7)+\pi(3^2)$

$SA=42\pi+9\pi=51\pi$

Find the surface area of the following partial cylinder.

Partial_cylinder

$234 \pi m^2 + 240m^2$

$240 \pi m^2 + 240m^2$

$234 \pi m^2 + 234m^2$

$234 \pi m^2 + 200m^2$

$200 \pi m^2 + 240m^2$

Explanation

The formula for the surface area of this partial cylinder is:

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

where is the radius of the cylinder, is the height of the cylinder, and is the sector of the cylinder.

Plugging in our values, we get:

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

$SA = 2(\pi (6m)^2)\left(\frac{270}{360}\right)+2(6m)(20m)+(2\pi (6m))\left(\frac{270}{360}\right)(20m)$

$SA = 54 \pi m^2 + 240m^2 +180 \pi m^2$

$SA = 234 \pi m^2 + 240m^2$

Find the surface area of the following partial cylinder.

Cylinder_sector

$\frac{104 \pi m^2}{3} + 80m^2$

$\frac{144 \pi m^2}{2} + 80m^2$

$144 \pi m^2+ 80m^2$

$\frac{80 \pi m^2}{3} + 144m^2$

$\frac{144 \pi m^2}{6} + 80m^2$

Explanation

The formula for the surface area of this partial cylinder is:

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

Where is the radius of the cylinder, is the height of the cylinder, and is the sector of the cylinder.

Plugging in our values, we get:

$SA = 2(\pi (8m)^2)\left(\frac{60}{360}\right)+2(8m)(5m)+(2 \pi (8m))\left(\frac{60}{360}\right)(5m)$

$SA = \frac{64 \pi m^2}{3} + 80m^2 + \frac{40 \pi m^2}{3}$

$SA = \frac{104 \pi m^2}{3} + 80m^2$

This figure is a right cylinder with radius of 2 m and a height of 10 m.

What is the surface area of the right cylinder (m2)?

Explanation

In order to find the surface area of a right cylinder you must find the area of both bases (the circles on either end) and add them to the lateral surface area. The area of the two circles is easy to find with $\pi r^{2}$ but remember to multiply by 2 for both bases

$2\cdot2^{2}\cdot\pi= 25.14$ .

Next find the lateral area. The lateral area if unrounded would be a rectangle with height of 10 m and length equal to the circumference of the base circles. Thus the lateral area is

$4\cdot\pi\cdot10= 125.66$