How to find the surface area of a cylinder - Math

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Question

What is the surface area of a cylinder of height in., with a radius of in?

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Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $4^2$ = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

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Question

What is the surface area of a cylinder having a base of radius in and a height of in?

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Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $11^2$ = \pi * 121$

You need to double this for the two bases:

$2 * 121 * \pi = 242 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 11* 3 = 66 * \pi$

Therefore, the total surface area is:

$242 * \pi + 66 * \pi = 308\pi$

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Question

What is the surface area of a cylinder with a height of in. and a diameter of in?

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Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. Notice, however that the diameter is inches. This means that the radius is . Now, the equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $2^2$ = \pi * 4$

You need to double this for the two bases:

$2 * 4 * \pi = 8 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 2 * 7 = 28 * \pi$

Therefore, the total surface area is:

$28\pi + 8\pi = 36\pi$

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Question

The volume of a cylinder with height of is $275\pi$ . What is its surface area?

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Answer

To begin, we must solve for the radius of this cylinder. Recall that the equation of for the volume of a cylinder is:

$V = \pi * $r^2$ * h$

For our values this is:

$275\pi = \pi * $r^2$ * 11$

Solving for , we get:

Hence,

Now, recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $5^2$ = \pi * 25$

You need to double this for the two bases:

$2 * 25 * \pi = 50 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 5 * 11 = 110 * \pi$

Therefore, the total surface area is:

$50\pi + 110\pi = 160\pi$

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Question

What is the surface area of a cylinder of height in, with a radius of in?

Tap to reveal answer

Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $4^2$ = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

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Question

Find the surface area of the following cylinder.

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Answer

The formula for the surface area of a cylinder is:

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

Where is the radius of the cylinder and is the height of the cylinder

Plugging in our values, we get:

$SA = 2\pi $(4m)^2$ + 2 \pi (4m)(9m)$

$SA = 104 \pi $m^2$$

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Question

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)?

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Answer

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

.

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

$4\cdot\pi\cdot10= 125.66$

Now add the lateral area to the area of the two bases:

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Question

Find the surface area of a cylinder given that its radius is 2 and its height is 3.2.

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Answer

The standard equation to find the surface area of a cylinder is

$Surface\ Area=2\pi $r^2$+2\pi rh$

where denotes the radius and denotes the height.

Plug in the given values for and to find the area of the cylinder:

$Area=2\pi $(2)^2$+2\pi (2)(3.2)=8\pi +12.8\pi =20.8\pi$

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Question

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?

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Answer

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$

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Question

Find the surface area of the following cylinder.

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Answer

The formula for the surface area of a cylinder is:

$SA = lateral\ area + 2\cdot (base)$

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

where is the radius of the base and is the length of the height.

Plugging in our values, we get:

$SA = 2 \pi (7m) (11m) + 2 \pi $(7m)^2$$

$SA = 154 \pi $m^2$ + 98 \pi $m^2$ = 252 \pi $m^2$$

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Question

Find the surface area of the following partial cylinder.

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Answer

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$$

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Question

Find the surface area of the following partial cylinder.

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Answer

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$$

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Question

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

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Answer

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

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

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

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Question

What is the surface area of a cylinder of height in., with a radius of in?

Tap to reveal answer

Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $4^2$ = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

← Didn't Know|Knew It →

Question

What is the surface area of a cylinder having a base of radius in and a height of in?

Tap to reveal answer

Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $11^2$ = \pi * 121$

You need to double this for the two bases:

$2 * 121 * \pi = 242 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 11* 3 = 66 * \pi$

Therefore, the total surface area is:

$242 * \pi + 66 * \pi = 308\pi$

← Didn't Know|Knew It →

Question

What is the surface area of a cylinder with a height of in. and a diameter of in?

Tap to reveal answer

Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. Notice, however that the diameter is inches. This means that the radius is . Now, the equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $2^2$ = \pi * 4$

You need to double this for the two bases:

$2 * 4 * \pi = 8 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 2 * 7 = 28 * \pi$

Therefore, the total surface area is:

$28\pi + 8\pi = 36\pi$

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Question

The volume of a cylinder with height of is $275\pi$ . What is its surface area?

Tap to reveal answer

Answer

To begin, we must solve for the radius of this cylinder. Recall that the equation of for the volume of a cylinder is:

$V = \pi * $r^2$ * h$

For our values this is:

$275\pi = \pi * $r^2$ * 11$

Solving for , we get:

Hence,

Now, recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $5^2$ = \pi * 25$

You need to double this for the two bases:

$2 * 25 * \pi = 50 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 5 * 11 = 110 * \pi$

Therefore, the total surface area is:

$50\pi + 110\pi = 160\pi$

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Question

What is the surface area of a cylinder of height in, with a radius of in?

Tap to reveal answer

Answer

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * $r^2$$

For our problem, this is:

$\pi * $4^2$ = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

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Question

What is the surface area of a cylinder with diameter 4 and height 6? The equation to calculate the surface area of a cylinder is:

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Answer

If the diameter of the cylinder is 4, the radius is equal to 2. Therefore:

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Question

A cylinder has a volume of 16 and a radius of 4. What is its height?

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Answer

Since the radius is 4, the area of the base is $16\pi$ . To cancel out the $\pi$ , the height must be $\frac{1}{\pi }$ .

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