Chapter 1,3 Page 34: Question 17

Question: The hollow passages through which smoke and fumes escape in a chimney are called flues. Each flue shown is 2cm thick, 20 cm high, and has a square opening that is 20cm by 20 cm.

a) What are the outside dimensions of the two flues?
b) If the height of each flue is 30cm, what is the outside surface area of the two flues? Hint: Do not forget the flat edges at the top. 



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SOLUTION

• Since each flue shown is 2cm thick, and the given opening is 20cm by 20cm, we know that it doesn't really give us the width of one flue.
• One flue will be 24cm because you are adding the 2cm from each side and adding the width from the given opening.
• Dimensions are width x height (24cm x 20cm)
• 20cm + 2(2cm) = 24cm

Answer: The outside dimensions of the two flues are 24cm(width) by 20cm(height).

• Before we start, to make it easier we should be able to change the image so it cooperates with the given description for the flue. 
• Instead of 20cm, I changed it to 30cm. The length will be 24cm because I used the same method. [ 20cm + 2(2cm) ] 
• However, for the width of the two flues together, it is 48cm because I doubled 24cm because there are two flues, not one.

SA= lw + 2( lh+hw ) - 2( lw )

     = (24cm)(48cm) + 2 [ (24cm)(30cm) + (30cm)(48cm) ] - 2[(20cm)(20cm)

     = 1152cm² + 2( 720cm² + 1440cm² ) - 2(400cm²)

     = 1152cm² + 2(2160cm²) - 800cm²

     = 1152cm² + 4320cmm² - 800cm²

     = 5472cm² - 800cm²

     = 4672cm²

Answer: The surface area of the two flues is 4672cm².

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