Question

unit review - surface area and volume

find the total surface area of the cylinder.

\\(sa = ?\text{ cm}^2\\)
round to the nearest hundredth
use 3.14 for \\(\pi\\)

Explanation:

Identify the given dimensions

We are given a cylinder with the following measurements:

• Radius \(r = 2\text{ cm}\)
• Height \(h = 7\text{ cm}\)
• Value of \(\pi \approx 3.14\)

State the surface area formula

The total surface area (\(SA\)) of a cylinder is the sum of the areas of its two circular bases and its curved lateral surface:

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

Calculate the area of the two bases

Substitute the given values into the base area term:

$$2\pi r^2 = 2 \cdot 3.14 \cdot 2^2$$

$$2\pi r^2 = 2 \cdot 3.14 \cdot 4 = 25.12\text{ cm}^2$$

Calculate the lateral surface area

Substitute the given values into the lateral area term:

$$2\pi rh = 2 \cdot 3.14 \cdot 2 \cdot 7$$

$$2\pi rh = 12.56 \cdot 7 = 87.92\text{ cm}^2$$

Sum the areas for total surface area

Add the base area and lateral area together:

$$SA = 25.12 + 87.92 = 113.04\text{ cm}^2$$

Answer:

Find the total surface area of the cylinder.

\(SA =\) <blank>113.04</blank> \(\text{cm}^2\)