Below is a net of a cylinder showing the formulas needed to find the areas of the circles and the rectangle.

Answer the Following Questions

• In order to find the total surface area of the cylinder, the areas of the two __?__ and the rectangle are added together.
  
  Interactive popup. Assistance may be required. Check Your Answer circles
  
  
• The formula for the area of a circle is ___?____.
  
  Interactive popup. Assistance may be required. Check Your Answer A = Pi r²
  
  
• The formula for the area of a rectangle is ___?____.
  
  Interactive popup. Assistance may be required. Check Your Answer A = l · w = b · h
  
  
• The length of the rectangle is the ____?_____ of the circle.
  
  Interactive popup. Assistance may be required. Check Your Answer circumference
  
  
• The formula for the circumference is ____?_____  where d is the diameter.
  
  Interactive popup. Assistance may be required. Check Your Answer c = dπ
  
  
• The new formula for the area of the rectangle is ___?___.
  
  Interactive popup. Assistance may be required. Check Your Answer A = circumference · height = dπ · h
  
  
• The formula for the total surface area of a cylinder is ____?____ .
  
  Interactive popup. Assistance may be required. Check Your Answer S = 2πr² + (dπ · height)

The formula for the surface area of a cylinder is:

S = 2πr² + (πd · height)

The diameter is twice the radius. Therefore another equation for the total area of a cylinder is below in terms of the radius, r, instead of the diameter, d.

Watch this video summarizing the formula of the surface area of a cylinder!

Example: Rappin’ Wrappers makes cylindrical cardboard tubes for shipping maps and other large documents. When constructing their containers they allow an additional 10% of material for the extra material needed to overlap the seams where the tubes are glued together and for the rim around the top.

If a company wants to order 50 cardboard shipping tubes that measure 4 inches in diameter and 28 inches long, how much material should Rappin’ Wrappers order?

Answer the following questions.

• The radius of the circle is ___?___ inches.
  
  Interactive popup. Assistance may be required. Check Your Answer 2
  
  
• The height of the tube is ___?____ inches.
  
  Interactive popup. Assistance may be required. Check Your Answer 28
  
  
• The total surface area of the cylinder is ___?___.
  
  Interactive popup. Assistance may be required. Check Your Answer 2πr² + 2πrh = 2(π)(2 in.)² + 2π(2 in.)(28 in.) = 8π in. + 112π in. = 120π in.².
  
  
• Substitute in 3.14 for π. The total surface area of the cylinder is approximately ___?___.
  
  Interactive popup. Assistance may be required. Check Your Answer 377 in²

Red Alert!!!

This is NOT the answer! Remember, the customer is ordering 50 shipping tubes or cylinders. Also, the Rappin’ Wrappers needs an extra 10% for the additional material. This is critical information to know, but it does not answer the question we were asked!

First, find the lateral area of 50 shipping tubes. (Use the rounded value of 377 in.2)

• Find the total surface area for 50 tubes.
  
  Interactive popup. Assistance may be required. Check Your Answer S = 50(377 in.²) = 18,850 in.²
  
  
• Select one of the two different ways to find the extra percentage of materials needed below to find the extra percentage and the total amount of material needed.
  
  
• Find 10% of the surface area.
  
  Interactive popup. Assistance may be required. Check Your Answer S = 18,850 in.²(.10) = 1,885 in.²
  
  
• Add the extra 10% to the total surface area of the 50 tubes.
  
  Interactive popup. Assistance may be required. Check Your Answer S = 18,850 in.² + 1,885 in.² = 20,735 in.²
  
  
• Since the total amount will be 110% of the total surface area, find 110% of the surface area.
  
  Interactive popup. Assistance may be required. Check Your Answer S = 1.10(18,850 in.²) = 20,735 in.²
  
  
• The company orders the material either in square feet or yards instead of square inches. Determine the materials needed in square feet.
  
  
• To find the number of square feet needed, divide the above answer by
  
  
• The amount of material needed in square feet is ____?____.
  
  Interactive popup. Assistance may be required. Check Your Answer

Determine the materials needed in square yards.

• To find the number of square yards needed divide the original answer by
• The amount of material needed in square yards is _____?_____.
  
  Interactive popup. Assistance may be required. Check Your Answer