Surface Area of Cylinders Practice Worksheet

Let's solve each problem step by step from the worksheet titled "Surface Area of Cylinders Practice".

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Problem 1:

> Jacob uses an empty can for a project, as shown below. He peels the label off the can and finds the area of the label. What is the approximate area of the can label?

Given:
- Height of the cylinder = 8 in
- Diameter of the base = 4 in → Radius $ r = \frac{4}{2} = 2 $ in

The label wraps around the side of the can — this is the lateral surface area of the cylinder.

Formula for lateral surface area:
$$
A_{\text{lateral}} = 2\pi r h
$$

Plug in the values:
$$
A = 2\pi (2)(8) = 32\pi
$$

Using $ \pi \approx 3.14 $:
$$
A \approx 32 \times 3.14 = 100.48 \text{ in}^2
$$

So, the area of the label is approximately 100.5 in².

✔ Answer: B) 100.53 in²

(They likely used $ \pi \approx 3.1416 $, so $ 32\pi \approx 100.53 $)

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Problem 2:

> A cylinder has a radius of 7 cm and a height of 10 cm. Find the total surface area of the cylinder.

Total Surface Area Formula:
$$
A_{\text{total}} = 2\pi r^2 + 2\pi r h
$$

Where:
- $ r = 7 $ cm
- $ h = 10 $ cm

First, calculate:
- $ 2\pi r^2 = 2\pi (7)^2 = 2\pi (49) = 98\pi $
- $ 2\pi r h = 2\pi (7)(10) = 140\pi $

Add them:
$$
A = 98\pi + 140\pi = 238\pi
$$

Now approximate using $ \pi \approx 3.14 $:
$$
A \approx 238 \times 3.14 = 747.32 \text{ cm}^2
$$

So, the total surface area is approximately 747.32 cm².

But let’s check the answer choices:

> A) $ 2\pi(7)^2 + 2\pi(7)(10) $
> B) $ 2\pi(7)^2 + 2\pi(7)(10) $
> C) $ 2\pi(7)^2 + 2\pi(7)(10) $
> D) $ 2\pi(7)^2 + 2\pi(7)(10) $

Wait — all options are the same? That seems like a typo.

But looking at the image, it says:

> A) $ 2\pi(7)^2 + 2\pi(7)(10) $
> B) $ 2\pi(7)^2 + 2\pi(7)(10) $
> C) $ 2\pi(7)^2 + 2\pi(7)(10) $
> D) $ 2\pi(7)^2 + 2\pi(7)(10) $

All are identical — probably a formatting error.

But since they’re all the same, the correct expression is:
$$
\boxed{2\pi r^2 + 2\pi r h}
$$

So any of the options A–D is correct if they're all the same.

But likely, the intended answer is:

✔ Answer: A) $ 2\pi(7)^2 + 2\pi(7)(10) $

(That’s the standard form.)

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Problem 3:

> Which expression shows the total surface area of a cylinder with a diameter of 2 inches and a height of 7 inches?

Given:
- Diameter = 2 in → Radius $ r = 1 $ in
- Height $ h = 7 $ in

Total Surface Area Formula:
$$
A = 2\pi r^2 + 2\pi r h
$$

Substitute:
- $ r = 1 $, $ h = 7 $
- $ A = 2\pi(1)^2 + 2\pi(1)(7) = 2\pi + 14\pi = 16\pi $

Now check the options:

> A) $ 2\pi(7)^2 + 2\pi(7)(2) $ → Wrong (uses 7 as radius, 2 as height)
> B) $ 2\pi(1)^2 + 2\pi(1)(7) $ → ✔ Correct!
> C) $ 2\pi(7)^2 + 2\pi(7)(2) $ → Same as A, wrong
> D) $ 2\pi(2)^2 + 2\pi(2)(7) $ → Uses diameter as radius, incorrect

So the correct expression is:
$$
2\pi(1)^2 + 2\pi(1)(7)
$$

✔ Answer: B) $ 2\pi(1)^2 + 2\pi(1)(7) $

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Problem 4:

> If a 6-inch strip is cut off the top of the cylinder, what would be the new total surface area of the cylinder?

Given:
- Original height = 14 in
- Cut off 6 in → New height = $ 14 - 6 = 8 $ in
- Radius = 4 in (from diagram)

We need to find the new total surface area.

Formula:
$$
A = 2\pi r^2 + 2\pi r h
$$

New $ h = 8 $ in, $ r = 4 $ in

Calculate:
- $ 2\pi r^2 = 2\pi (4)^2 = 2\pi (16) = 32\pi $
- $ 2\pi r h = 2\pi (4)(8) = 64\pi $
- Total: $ 32\pi + 64\pi = 96\pi $

Now approximate:
$$
96\pi \approx 96 \times 3.14 = 300.24 \text{ in}^2
$$

So, new total surface area ≈ 300.24 in²

But we must consider: Is the top removed?

The problem says "a 6-inch strip is cut off the top" — this means the height is reduced, but the top circular face is removed.

Wait — important point:

- The original cylinder had two bases.
- If you cut off a 6-inch strip from the top, you are removing a portion of the cylinder, but the top base is no longer there.
- However, the cut creates a new flat circular face at the top.

So actually, the number of bases remains two: the bottom base and the new top face.

So the surface area includes:
- Two circular bases (both radius 4 in)
- Lateral surface area with height 8 in

Thus, the formula still applies:
$$
A = 2\pi r^2 + 2\pi r h = 2\pi(4)^2 + 2\pi(4)(8) = 32\pi + 64\pi = 96\pi
$$

So yes, the new total surface area is $ 96\pi $ in², or about 300.24 in².

✔ Answer: $ 96\pi $ in² or approximately 300.24 in²

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✔ Final Answers Summary:

1. B) 100.53 in²
2. A) $ 2\pi(7)^2 + 2\pi(7)(10) $
3. B) $ 2\pi(1)^2 + 2\pi(1)(7) $
4. $ 96\pi $ in² (or ~300.24 in²)

Let me know if you'd like these written neatly on the worksheet!