Question

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 ?.

Answer 1

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 \[ 1: \frac{\pi}{4}:\frac{1}{2} \]

Answer 2

but in my homework paper it say a hint;use 2r to represent the length of the sides of the square

Answer 3

right, since I used 'a' letter representing the side of the square
We should obtain the same answer

Answer 4

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 ?.

Answer 5

and when u done with that can u help me with http://openstudy.com/groups/mathematics/updates/4dd44da8d95c8b0b59f756c4

Answer 6

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
\[ V_3= \pi \frac{a^3}{4} \]

Answer 7

if you feel less comfortable with 'a', you can replace it by '2r' as in a hint to obtain the answer

Answer 8

It's \[ \frac{1}{4} : \frac{1}{3} : \frac{1}{12} \]

Answer 9

so what the answer of ? to ? to ? for b..

Answer 10

oh okay