Cones, Cylinders, & Spheres Unit Test

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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.(1 point)
ft2
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Answer 1

To find the surface area \( A \) of a cylinder, you can use the formula:

\[ A = 2\pi r(h + r) \]

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

For Adrian's cylinder:

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

Plug these 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: \[ A = 2 \times 3.14 \times 4 \times 7 \]

3. Calculate \( A \): \[ A = 2 \times 3.14 \times 4 \times 7 = 2 \times 3.14 \times 28 \] \[ A = 2 \times 87.92 = 175.84 \]

Finally, rounding to the nearest tenth gives: \[ A \approx 175.8 , \text{square feet} \]

So, the surface area of the cylinder is approximately 175.8 ft².