Think About the Process  A manufacturer produces cylindrical cans of fruit as shown. To use a formula to find the surface area of each​ can, you need to find the radius of each can. What step should you perform to find the radius of each​ can? Use a formula to find the surface area of each can. Use 3.14 for pi.

3 and seven eighths in.
6 and one fourth in.
​(The figure is not to​ scale.)
Question content area bottom
Part 1
What step should you perform to find the radius of each​ can?
A.
Divide 3seven eighths
by 2.
B.
Multiply 3seven eighths
by 2.
C.
Divide 6one fourth
by 2.
D.
Multiply 6one fourth
by 2.

1 answer

To find the radius of each can, you need to find half of the diameter for each can. The diameter is represented by the height measurement in this context, as it refers to the cylindrical can's diameter when measuring across the circular top or base.

For the given dimensions:

  1. 3 and seven eighths inches (which can be interpreted as the diameter of the can)
  2. 6 and one fourth inches (also likely referring to the height of the can instead of diameter since the surface area would typically involve the radius based on the top/bottom area of the cylinder).

Here’s how to determine the radius for the can based on the dimensions given:

Step to find the radius:

  • For option A: Divide 3 and seven eighths by 2.
  • For option C: Divide 6 and one fourth by 2.

To find the radius from the diameter:

  • You would use option A for the first measurement.

Thus, the correct step to find the radius of each can, based on the relevant diameter from the information provided, is: A. Divide 3 and seven eighths by 2.

Now, let's calculate the radius and then use it to find the surface area of the can:

  1. Convert mixed numbers to improper fractions:

    • \(3 \frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}\)
  2. Finding the radius:

    • Radius \(r = \frac{31/8}{2} = \frac{31}{16}\)
  3. Surface Area of a Cylinder: The formula for the surface area \(A\) of a cylinder is: \[ A = 2\pi r^2 + 2\pi rh \] Where \(h\) is the height of the cylinder.

  4. Calculate using \(\pi = 3.14\): Assuming the height given (6 and one fourth) refers to the height \(h\) of the can:

    • Height \(h = 6 \frac{1}{4} = \frac{25}{4}\)
  5. Substituting values: \[ A = 2(3.14)(\frac{31}{16})^2 + 2(3.14)(\frac{31}{16})(\frac{25}{4}) \]

    Calculate \(r^2\) (the radius squared), \(2\pi r^2\), and \(2\pi rh\) separately to find the total surface area.

    • Calculate \( \left(\frac{31}{16}\right)^2 = \frac{961}{256}\) \(2 \times 3.14 \times \frac{961}{256}\)
    • Calculate \(2 \times 3.14 \times \frac{31}{16} \times \frac{25}{4}\)

Finally, sum these two computed areas to complete the surface area calculation.

Feel free to perform the numerical calculations or let me know if you need help with them!