Now, let’s apply the formulas to solve real-world problems.

Example: A cone shaped container was designed to transport a perfectly shaped evergreen tree to another state. The diameter of the tree is 8 ft. The height of the tree is 20 feet. Find the surface area of the container created to transport the tree.

• The radius of the circular base is ___?___.
  
  Interactive popup. Assistance may be required. Check Your Answer 4 feet
  
  
• The height of the tree is ___?___.
  
  Interactive popup. Assistance may be required. Check Your Answer 20 feet
  
  
• The Pythagorean Theorem is used to find the slant height. State the Pythagorean Theorem.
  
  Interactive popup. Assistance may be required. Check Your Answer a² + b² = c²
  

State the given values for the cone above.

• a = 4;
• a² = ___?___
  
  Interactive popup. Assistance may be required. Check Your Answer 16
  
  
• b = 20
  
• b² = ____?___
  
  Interactive popup. Assistance may be required. Check Your Answer 400
  
  
• Fill in the values for the Pythagorean Theorem to find c.
  
  Interactive popup. Assistance may be required. Check Your Answer 16 + 400 = c²
  416 = c²
  √416 ≈ 20.4
  
  
• The total surface area of the container is ____?_____.
  
  Interactive popup. Assistance may be required. Check Your Answer S = πrl + πr²
  = π(4 ft)(20.4 ft) + π(4 ft)²
  = 81.6π ft² + 16π ft²
  = 97.6π ft² ≈306.5 ft²