A cube with edges of length 6\sqrt{3} is inscribed in a sphere with a volume of a\pi. What is the value of a ?

Note: The formula for the volume of a sphere is V=\dfrac{4}{3}\pi r^3.



In the equation above, a, b, and c are constants. If the equation represents a circle with center (5,-2) and radius 7, what is the value of c ?


In the figure above, quadrilateral PQST is divided into three non-overlapping right triangles. the length of \overline{QR} is 12, the length of \overline{QS} is 13, and the length of \overline{ST} is 4. What is the length of \overline{PT} ?


In the xy-plane, line n passes through the origin and intersects line m at the point (10, 2). Line m is perpendicular to line n. What is the value of the x-intercept of line m ?


In the xy-plane, (a,b) and (c,d) are the points of intersection between the graphs of y=x+3 and y=x^2-3. What is the value of a+b+c+d ?


Section progress