We want to wrap this cylinder in gift wrapping paper. What is the total surface area rounded to the nearest hundredth?

a cylinder with a radius of 3 and a height of 2

answers:

150 ft^2

94.25 ft^2

194.25 ft^2

56.55 ft^2

1 answer

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

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

where:

  • \(r\) is the radius of the cylinder
  • \(h\) is the height of the cylinder

Given:

  • radius \(r = 3\) ft
  • height \(h = 2\) ft

Now substituting the values:

\[ A = 2\pi (3)(2 + 3) \] \[ A = 2\pi (3)(5) \] \[ A = 2\pi (15) \] \[ A = 30\pi \]

Now, using \( \pi \approx 3.14 \):

\[ A \approx 30 \times 3.14 = 942 \]

However, since we need the total surface area rounded to the nearest hundredth in square feet, we calculate more accurately:

Using \( \pi \approx 3.14159 \):

\[ A \approx 30 \times 3.14159 = 94.2477 \]

So, rounding to the nearest hundredth, the total surface area is:

\[ A \approx 94.25 \text{ ft}^2 \]

Hence, the correct answer is:

94.25 ft².