SAT Math: Geometry and Trigonometry

A cube has an edge length of $68$ inches. A solid sphere with a radius of $34$ inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

A sphere has a radius of $\frac{17}{5}$ feet. What is the volume, in cubic feet, of the sphere?

The length of the edge of the base of a right square prism is $6$ units. The volume of the prism is $2,880$ cubic units. What is the height, in units, of the prism?

What is the diameter of the circle in the $xy$-plane with equation $(x-5)^2 + (y-3)^2 = 16$?

A circle in the xy-plane has its center at $(-4, -6)$. Line $k$ is tangent to this circle at the point $(-7, -7)$. What is the slope of line $k$?

In the figure, two lines intersect at a point. Angle $1$ and angle $2$ are vertical angles. The measure of angle $1$ is $72^{\circ}$. What is the measure of angle $2$?

A circle has center $G$, and points $M$ and $N$ lie on the circle. Line segments $MH$ and $NH$ are tangent to the circle at points $M$ and $N$, respectively. If the radius of the circle is $168$ millimeters and the perimeter of quadrilateral $GMHN$ is $3,856$ millimeters, what is the distance, in millimeters, between points $G$ and $H$?