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Philip Calvert

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  1. The answer for 6a is 4r + (pi x r). I don't understand how pi is used here. Two curves surround two sides of the square, but I don't understand how this fact is identified as "pi x r".
  2. Just a quick one here: the Answer Key I have gives only the area, but not the perimeter, and the book asks for both. We calculated the perimeter as 82.82 cm. Is that correct?
  3. For this one, I'm confused about how to explain it. 7 is the radius I'm pretty sure, but the tricky part is that the quarter circle is larger than the semi-circle. Therefore, multiplying 22/7 by 49 and by 1/2 produces 77. Multiplying 22/7 by 49 and by 1/4 produces 38.5, so it would seem the ratio of A:B is 2:1. I know the opposite is true, but I'm stuck on how to explain this. Could you please assist?
  4. We correctly calculated the volume of the syrup as 715.4 inches cubed in 7a, but were unsuccessful with 7b: 1/2 x 20 (base) x 9 (height) x 15 (Height) = 1 350. The difference between the volume of the container and of the syrup is 1 350 - 715.4 = 634.4, but the book's answer is 8! What have we done incorrectly?
  5. I think the volume of the rectangle is 7 x 14 x 42 = 4 116, and the volume of the semi-circle is 3.14 x 49 x 42 = 6 462.1. Four rectangles in the float means 4 116 x 4 = 16 464, and three semi-circles means 6 462.1 x 3 = 19 386.3. Adding these two products gives us 35 850.3, which is a long way from the textbook's answer of 26 166 inches cubed. Could you please assist Jenny?
  6. Philip Calvert

    Textbook 6B, Practice A, page 39, 4a and b

    Ouch! Sorry about that. In any case, the difference between the volumes of the two shapes we found to be 5192.8 - 750 = 4442.8, which is still a bit off from the book's answer of 4447.5. Do you think this difference in the answers is significant?
  7. Thanks for letting me know ... .
  8. Hi Jenny, We got the answer to 5b, so our difficulty with 5a surprised us. We calculated the volume of the triangular prism as 10 (base) x 15 (height of triangle) x 20 (height of prism) divided by 2 = 1500 cubic cm. The solid rectangular prism we found as 5 x 10 x 20 = 1000 cubic cm. The circular holes was pi x 4 squared x 10 (height of each hole) = 502.9 x 3 holes = 1508.7 Obviously, we can't subtract the figure we got for the circular holes from the solid rectangular prism. What have we done wrong?
  9. Hi Jenny, My son and I had no problem identifying the answer for 4a as "Shape B", but the answer given for 4b indicates that our calculations for shapes A or B or both were incorrect. For shape A, we calculated the volume as 20 (base) x 5 (height of the triangular base) x 15 (height of the prism) and divide by 2 = 225 cubic in. For shape B, we calculated the volume as pi x 10.5 squared x 15 (height of the prism) = 5192.8 cubic in. 4b asks us to find the difference of the volume of these two shapes, which we found as 4967.8; the book's answer is 4447.5 cubic in. What have we done wrong?
  10. Philip Calvert

    6B Textbook page 27, number 5

    Indeed, thank you. I see that all one need do to calculate perimeter is to identify the length of curve.
  11. I'm afraid I missed something in finding the area, so I can't find the perimeter either. I calculated the radius as five squared, multiplied it by pi and divided by 4. I then doubled what I thought was the area, and got 39.2, which isn't even close to the workbook's answer of 57. Could you please help?
  12. Philip Calvert

    Textbook 6A page 149, Ex. 7

    I appreciate the help!