Simone has a red cylindrical storage box that she would like to decorate with patterned paper. How much paper will Simone need to cover the entire box? Use 3.14 for π.

Determine the total surface area of the shape. Remember to not round the answers.

(7 points)
Radius of circle =
inches Area of each Circular Face =
square inches

Total Area of the Circular Faces =
square inches

Circumference of Circle =
inches Height of Cylinder =
inches

Area of the Lateral Face =
square inches

Total Surface Area of Cylinder =
square inches

1 answer

To calculate the total surface area of a cylinder, we need the radius of the circular base and the height of the cylinder. However, the measurements for these parameters are not provided in your question. Please provide the radius and height of the cylindrical storage box to calculate the surface area correctly.

Once we have that information, we can proceed with the following steps:

Step 1: Calculate the Area of Each Circular Face

  • Area of Each Circular Face (A): \[ A = \pi r^2 \] where \( r \) is the radius of the base.

Step 2: Calculate the Total Area of the Circular Faces

  • Total Area of the Circular Faces (TA): \[ TA = 2A = 2(\pi r^2) \]

Step 3: Calculate the Circumference of the Circle

  • Circumference (C): \[ C = 2\pi r \]

Step 4: Calculate the Area of the Lateral Face (Side)

  • Area of the Lateral Face (L): \[ L = C \times h = (2\pi r) \times h \]

Step 5: Calculate the Total Surface Area of the Cylinder

  • Total Surface Area (SA): \[ SA = TA + L = 2\pi r^2 + 2\pi rh \]

Now if you can provide the radius \( r \) and the height \( h \) of the cylinder, I can proceed with the calculations and complete the answers for the surface area of the cylinder!