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 three fourths in.
4 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.
Multiply 3three fourths
by 2.
B.
Divide 4one fourth
by 2.
C.
Divide 3three fourths
by 2.
D.
Multiply 4one fourth
by 2.

1 answer

To find the radius of a cylindrical can when given the diameter, you should divide the diameter by 2.

From your options, you need to first determine which measurement represents the diameter. Assuming that 3 and three fourths inches (3.75 inches) refers to the height of the can and 4 and one fourth inches (4.25 inches) refers to the diameter of the can, you would need to select the appropriate option.

Given:

  • Diameter = 4 and one fourth inches = 4.25 inches

To find the radius:

  • Radius = Diameter ÷ 2

Thus, you would perform the following step: B. Divide 4 and one fourth by 2.

Now, the radius would be: \[ \text{Radius} = 4.25 \div 2 = 2.125 \text{ inches} \]

Next, to find the surface area of the can, you can use the formula for the surface area of a cylinder, which is:

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

where:

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

Substituting the values:

  • \( r = 2.125 \) inches,
  • \( h = 3.75 \) inches:

\[ \text{Surface Area} = 2 \times 3.14 \times 2.125 \times (3.75 + 2.125) \]

First calculate \( (3.75 + 2.125) \): \[ 3.75 + 2.125 = 5.875 \]

Now calculate the surface area: \[ \text{Surface Area} = 2 \times 3.14 \times 2.125 \times 5.875 \]

Calculating step-by-step:

  1. \( 2 \times 2.125 = 4.25 \)
  2. \( 4.25 \times 5.875 = 24.9375 \)
  3. \( 24.9375 \times 3.14 \approx 78.21875 \)

Thus, the surface area of the can is approximately \( 78.22 \) square inches (rounded to two decimal places).