anonymous
  • anonymous
Greek mathematician Archimedes liked the design at right so much that he wanted it on his tombstone. a.Calculate the ratio of the area of the square, the area of the circle, and the area of the isosceles triangle. Copy and complete this statement of proportionality. Area of square to Area of circle to Area of triangle is ? to ? to ?.
Mathematics
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
Area of the square \[ a^2\] The area of the circle \[ \pi\frac{a^2}{4} \] Area of the isosceles triangle \[ \frac{a^2}{2} \] Hence, the complete statement should be read as follows Area of square to Area of circle to Area of triangle is \[ 1: \frac{\pi}{4}:\frac{1}{2} \]
anonymous
  • anonymous
but in my homework paper it say a hint;use 2r to represent the length of the sides of the square

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anonymous
  • anonymous
right, since I used 'a' letter representing the side of the square We should obtain the same answer
anonymous
  • anonymous
b.When each of the figures is revolved about the vertical line of symmetry, it generates a solid of revolution—a cylinder, a sphere, and a cone. Calculate their volumes. Copy and complete this statement of proportionality. Volume of cylinder to Volume of sphere to Volume of cone is ? to ? to ?.
anonymous
  • anonymous
anonymous
  • anonymous
right, the formula to calculate the cone is \[ V_1=\frac{\pi a^3}{12} \] Volume for the sphere using the formula is \[ V_2=\frac{\pi a^3}{3} \] And lastly, volume of the cylinder is \[ V_3= \pi \frac{a^3}{4} \]
anonymous
  • anonymous
if you feel less comfortable with 'a', you can replace it by '2r' as in a hint to obtain the answer
anonymous
  • anonymous
It's \[ \frac{1}{4} : \frac{1}{3} : \frac{1}{12} \]
anonymous
  • anonymous
so what the answer of ? to ? to ? for b..
anonymous
  • anonymous
oh okay

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