Cones, Cylinders, & Spheres Unit Test

Question

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Question
Adrian is painting the outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet. Adrian wants to paint all around the outside of the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface are of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? Use 3.14 for pi and round your answer to the nearest tenth.

Answer 1

To find the surface area of a cylinder, you can use the formula:

\[ \text{Surface Area} = 2\pi r(h + r) \]

where \( r \) is the radius and \( h \) is the height of the cylinder.

Given:

• Radius (\( r \)) = 4 feet
• Height (\( h \)) = 3 feet
• \( \pi \approx 3.14 \)

Now, plug in the values into the formula:

1. Calculate \( h + r \): \[ h + r = 3 + 4 = 7 \]

2. Now substitute \( r \) and \( h + r \) into the surface area formula: \[ \text{Surface Area} = 2 \times 3.14 \times 4 \times 7 \]

3. Calculate \( 2 \times 3.14 = 6.28 \): \[ \text{Surface Area} = 6.28 \times 4 \times 7 \]

4. Calculate \( 4 \times 7 = 28 \): \[ \text{Surface Area} = 6.28 \times 28 \]

5. Now calculate \( 6.28 \times 28 \): \[ 6.28 \times 28 = 176.84 \]

Rounding to the nearest tenth, the surface area is:

\[ \text{Surface Area} \approx 176.8 \text{ square feet} \]

Thus, the surface area of the outside of the cylinder is approximately 176.8 square feet.