## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 2

Geometry and Measurement

2.2 Three-Dimensional Geometry

### Answers and Explanations

Surface Area and Volume

1. **(C)** The volume of the cube is *x*^{3}. The radius of the cylinder is , and its height is *x* . Substitute these into the formula for the volume of a cylinder:

2. **(C)*** V* = π*r*^{2}*h*, and total area = 2π*r*^{2} + 2π*rh* . Setting these two equal yields *rh* = 2*r* + 2*h* . Therefore, . Since *h* must be positive, the smallest integer value of *r* is 3.

3. * **(D)** The length of the longest segment is

Coordinates in Three Dimensions

1. **(D)** The square of the distance between *P* and *Q* is 9, so

(*x* – 3)^{2} + (–1 – (–3))^{2} + (–1 – 1)^{2} = 9, or (*x* – 3)^{2} = 1.

Therefore, *x* – 3 = ±1, so *x* = 2 or 4.

2. **(D)** Since the *y* -coordinate is zero, the point must lie in the *xz* plane.

3. * **(C)** The line 3*x* + 2*y* = 7 has *x* -intercept and *y* -intercept . The part of this line that lies in the first quadrant forms a triangle with the coordinate axes. Rotating this triangle about the *x* -axis produces a cone with radius and height . The volume of this cone is .