Question

Deena has a set of 4 coasters on her coffee table, and each coaster is shaped like a cylinder with a height of 0.5 inches and a radius of 2.5 inches. Which is the total surface area of the 4 coasters?
5 points
A. 7.85 inches squared
B. 47.1 inches squared
C. 31.4 inches squared
D. 188.4 inches squared

Answer 1

To find the total surface area of the 4 coasters, we first need to calculate the surface area of a single cylindrical coaster.

The formula for the total surface area \(A\) of a cylinder is:

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

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

Given:
- Height \(h = 0.5\) inches
- Radius \(r = 2.5\) inches

Now we can plug in the values:

\[
A = 2\pi (2.5)(0.5 + 2.5)
\]

First, calculate \(0.5 + 2.5\):

\[
0.5 + 2.5 = 3
\]

Now substitute this value back into the formula:

\[
A = 2\pi (2.5)(3)
\]

Calculate \(2.5 \times 3\):

\[
2.5 \times 3 = 7.5
\]

Now we have:

\[
A = 2\pi (7.5) = 15\pi
\]

Using \(\pi \approx 3.14\):

\[
A \approx 15 \times 3.14 = 471
\]

So the surface area of one coaster is approximately \(47.1\) square inches.

Since Deena has 4 coasters, we multiply this area by 4:

\[
\text{Total Surface Area} = 4 \times 47.1 = 188.4 \text{ square inches}
\]

Thus, the total surface area of the 4 coasters is:

\[
\boxed{188.4 \text{ inches squared}}
\]
And the correct answer is D. 188.4 inches squared.