ISEE Upper Level Word Problems: Miscellaneous Geometry and Visual Perception Practice Test 20

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1. The formula for the volume of a pyramid with a square base is Bh, where B represents the area of the square base of the pyramid and h represents the height of the pyramid. The volume of Pyramid A is one half the volume of Pyramid B. Which of the following statements could be true?

  • A. The height of Pyramid A is one half the height of Pyramid B, and a side of the base of Pyramid A is the two times a side of the base of Pyramid B.
  • B. The height of Pyramid A is one half the height of Pyramid B, and a side of the base of Pyramid A is the same as a side of the base of Pyramid B.
  • C. A side of the base of Pyramid A is one half a side of the base of Pyramid B, and the height of Pyramid A is the same as the height of Pyramid B.
  • D. Both a side and the height of Pyramid A are one half a side and the height of Pyramid B.

2. The surface area of a right circular cylinder is represented by SA = 2πr2 + 2πrh, where r is the radius of the cylinder and h is its height. If the surface area of a right circular cylinder is 36π and its radius is 3, what is its height?

  • A. 2
  • B. 3
  • C. 4
  • D. 5

3. Triangle ABC is shown. The length of is 3 inches. The measure of angle ACB is 35°.

Which expression gives the value of ?

  • A. 3 tan 35°
  • B. 3 cos 35°
  • C.
  • D.

4. What gives the number of square feet of tiles needed to cover a rectangular floor that is 3 yards long by 4 yards wide?

  • A. 12 ft2
  • B. 36 ft2
  • C. 48 ft2
  • D. 108 ft2

5. Use the cube to answer the question.

In the cube above, which corner is farthest from P?

  • A. Q
  • B. R
  • C. S
  • D. T

6. A square inscribed in a square is shown.

In terms of x, what is the length of line segment m?

  • A. 5x2
  • B. 13x2
  • C. x
  • D. x

7. A Venn diagram is shown.

In the Venn diagram, circle A represents all multiples of 4, and circle B represents all multiples of 7. Which of the following best describes the shaded region?

  • A. Multiples of 3
  • B. Multiples of 11
  • C. Multiples of 28
  • D. Multiples of 47

8. Use the cube to answer the question.

Which figure is a possible net for the cube?

  • A.
  • B.
  • C.
  • D.