Question

Marina is comparing the surface area of two soda cans. Can A has a diameter of 4 in
and a height of 5 in
while can B has a diameter of 3 in
and a height of 7 in
.

Which can has a greater surface area, and by how much? Use pi = 3.14
.


has a greater surface area by

Answer 1

To find the surface area of both cans, we can use the formula for the surface area of a cylinder:

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

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

### Can A
- Diameter = 4 in, so the radius \( r_A = \frac{4}{2} = 2 \) in
- Height \( h_A = 5 \) in

Substituting into the formula:

\[
\text{Surface Area}_A = 2\pi (2^2) + 2\pi (2)(5)
\]

Calculating each term:

1. \( 2\pi (2^2) = 2\pi (4) = 8\pi \)
2. \( 2\pi (2)(5) = 20\pi \)

Adding these together:

\[
\text{Surface Area}_A = 8\pi + 20\pi = 28\pi
\]

Substituting \(\pi = 3.14\):

\[
\text{Surface Area}_A = 28 \times 3.14 = 87.92 \text{ in}^2
\]

### Can B
- Diameter = 3 in, so the radius \( r_B = \frac{3}{2} = 1.5 \) in
- Height \( h_B = 7 \) in

Substituting into the formula:

\[
\text{Surface Area}_B = 2\pi (1.5^2) + 2\pi (1.5)(7)
\]

Calculating each term:

1. \( 2\pi (1.5^2) = 2\pi (2.25) = 4.5\pi \)
2. \( 2\pi (1.5)(7) = 21\pi \)

Adding these together:

\[
\text{Surface Area}_B = 4.5\pi + 21\pi = 25.5\pi
\]

Substituting \(\pi = 3.14\):

\[
\text{Surface Area}_B = 25.5 \times 3.14 = 80.007 \text{ in}^2
\]

### Conclusion
Now we can compare the surface areas:

- Surface Area of Can A: \( 87.92 \, \text{in}^2 \)
- Surface Area of Can B: \( 80.007 \, \text{in}^2 \)

To find the difference:

\[
\text{Difference} = 87.92 - 80.007 = 7.913 \, \text{in}^2
\]

**Final Answer**:
Can A has a greater surface area by **approximately 7.91 in²**.