Question

A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.

7.9

31.8

24.7

21.2

Answer 1

To find the surface area of the cylinder, we use the formula:

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

where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14.

1. First, we find the radius \( r \). The diameter of the cylinder is given as 1.5 cm, so the radius \( r \) is:

\[
r = \frac{\text{Diameter}}{2} = \frac{1.5 \text{ cm}}{2} = 0.75 \text{ cm}
\]

2. The height \( h \) is given as 4.5 cm.

3. Now we can plug the values into the surface area formula:

\[
\text{Surface Area} = 2 \cdot 3.14 \cdot 0.75 \cdot (4.5 + 0.75)
\]

Calculating \( (4.5 + 0.75) \):

\[
4.5 + 0.75 = 5.25
\]

4. Now substituting back into the formula:

\[
\text{Surface Area} = 2 \cdot 3.14 \cdot 0.75 \cdot 5.25
\]

First, calculate \( 2 \cdot 3.14 \):

\[
2 \cdot 3.14 = 6.28
\]

Next, calculate \( 0.75 \cdot 5.25 \):

\[
0.75 \cdot 5.25 = 3.9375
\]

Now multiply those results together:

\[
\text{Surface Area} = 6.28 \cdot 3.9375
\]

Calculating \( 6.28 \cdot 3.9375 \):

\[
6.28 \cdot 3.9375 = 24.7
\]

Thus, the surface area of the cylinder is \( 24.7 \) square centimeters.

The correct answer is \( \text{24.7} \).