Honors Geometry 2nd Semester Review Notes

Sphere Volume Ratios

  • The ratio of the volumes of two spheres can be calculated using the formula: Volume ratio=(Diameter ratio)3\text{Volume ratio} = \text{(Diameter ratio)}^3.

Equations of Circles

  • The standard equation of a circle is given as (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2, where (h,k)(h, k) is the center and rr is the radius.

  • To find the radius from the equation, you can isolate rr by taking the square root of both sides after rearranging the formula to r=extsqrt((x−h)2+(y−k)2)r = ext{sqrt}((x-h)^2 + (y-k)^2). This can also be rewritten in terms of the diameter as r=d2r = \frac{d}{2}, where dd is the diameter of the circle.