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Geometry Word Problems Practice Questions Set 6

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Updated on Sep 26, 2011

Geometry Word Problems

The geometry problems in this set  involve lines, angles, triangles, rectangles, squares, and circles. You will learn how to find length, perimeter, area, circumference, and volume, and how you can apply geometry to everyday problems.

  1. Find the area of the regular octagon with the following measurements.
  2. Geometry

    1. 224 square units
    2. 112 square units
    3. 84 square units
    4. 169 square units
  3. Two sides of a picture frame are glued together to form a corner. Each side is cut at a 45-degree angle. Using the illustration provided, find the measure of A.
  4. Geometry

    1. 45°
    2. 90°
    3. 115°
    4. 135°
  5. Find the total area of the shaded regions, if the radius of each circle is 5 cm. Leave answer in terms of π.
  6. Geometry

    1. 1,200 – 300π cm2
    2. 300 – 300π cm2
    3. 300 π – 1,200 cm2
    4. 300 π – 300 cm2
  7. The road from town A to town B travels at a direction of N23°E. The road from town C to town D travels at a direction of S48°E. The roads intersect at location E. Find the measure of BED, at the point of intersection.
    1. 71°
    2. 23°
    3. 109°
    4. 48°
  8. The figure provided below represents a hexagonal-shaped nut. What is the measure of ABC?
  9. Geometry

    1. 120°
    2. 135°
    3. 108°
    4. 144°
  10. If the lengths of all sides of a box are doubled, how much is the volume increased?
    1. 2 times
    2. 4 times
    3. 6 times
    4. 8 times
  11. If the radius of a circle is tripled, the circumference is
    1. multiplied by 3.
    2. multiplied by 6.
    3. multiplied by 9.
    4. multiplied by 12.
  12. If the diameter of a sphere is doubled, the surface area is
    1. multiplied by 4.
    2. multiplied by 2.
    3. multiplied by 3.
    4. multiplied by 8.
  13. If the diameter of a sphere is tripled, the volume is
    1. multiplied by 3.
    2. multiplied by 27.
    3. multiplied by 9.
    4. multiplied by 6.
  14. If the radius of a cone is doubled, the volume is
    1. multiplied by 2.
    2. multiplied by 4.
    3. multiplied by 6.
    4. multiplied by 8.
  15. If the radius of a cone is halved, the volume is
    1. multiplied by .
    2. multiplied by .
    3. multiplied by .
    4. multiplied by .
  16. If the radius of a right cylinder is doubled and the height is halved, its volume
    1. remains the same.
    2. is multiplied by 2.
    3. is multiplied by 4.
    4. is multiplied by .
  17. If the radius of a right cylinder is doubled and the height is tripled, its volume is
    1. multiplied by 12.
    2. multiplied by 2.
    3. multiplied by 6
    4. multiplied by 3.
  18. If each interior angle of a regular polygon has a measure of 150 degrees, how many sides does it have?
    1. 10
    2. 11
    3. 12
    4. 13
  19. A box is 30 cm long, 8 cm wide and 12 cm high. How long is the diagonal ? Round to the nearest tenth.
  20. Geometry

    1. 34.5 cm
    2. 32.1 cm
    3. 35.2 cm
    4. 33.3 cm
  21. Find the area of the shaded region. Leave answer in terms of π.
  22. Geometry

    1. 16.5π
    2. 30π
    3. 7.5π
  23. A round tower with a 40 meter circumference is surrounded by a security fence that is 8 meters from the tower. How long is the security fence in terms of π?
    1. (40 + 16π) meters
    2. (40 + 8π) meters
    3. 48π meters
    4. 56π meters
  24. The figure below is two overlapping rectangles. Find the sum of 1 + 2 + 3 + 4.
  25. Geometry

    1. 360°
    2. 90°
    3. 180°
    4. 540°
  26. A solid is formed by cutting the top off of a cone with a slice parallel to the base, and then cutting a cylindrical hole into the resulting solid. Find the volume of the hollow solid in terms of π.
  27. Geometry

    1. 834π cm3
    2. 2,880π cm3
    3. 891π cm3
    4. 1,326π cm3
  28. A rectangular container is 5 cm wide and 15 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. What is the volume of the object?
    1. 92 cm3
    2. 276 cm3
    3. 172.5 cm3
    4. 312.5 cm3
  29. A concrete retaining wall is 120 feet long with ends shaped as shown. How many cubic yards of concrete are needed to construct the wall?
  30. Geometry

    1. 217.8 yd3
    2. 5,880 yd3
    3. 653.3 yd3
    4. 49 yd3
  31. A spherical holding tank whose diameter to the outer surface is 20 feet is constructed of steel 1 inch thick. How many cubic feet of steel is needed to construct the holding tank? Round to the nearest integer value. (π = 3.14)
  32. Geometry

    1. 78 ft3
    2. 104 ft3
    3. 26 ft3
    4. 125 ft3
  33. How many cubic inches of lead are there in the pencil? Round to the nearest thousandth. (π = 3.14)
  34. Geometry

    1. .061 in3
    2. .060 in3
    3. .062 in3
    4. .063 in3
  35. A cylindrical hole with a diameter of 4 inches is cut through a cube. The edge of the cube is 5 inches. Find the volume of the hollowed solid in terms of π.
  36. Geometry

    1. 125 – 80π
    2. 125 – 20π
    3. 80π – 125
    4. 20π – 125
  37. Find the area of the region.
  38. Geometry

    1. 478 units2
    2. 578 units2
    3. 528 units2
    4. 428 units2
  39. From a stationary point directly in front of the center of a bull's eye, Kim aims two arrows at the bull's eye. The first arrow nicks one point on the edge of the bull's eye; the second strikes the center of the bull's eye. Kim knows the second arrow traveled 20 meters since she knows how far she is from the target. If the bull's eye is 4 meters wide, how far did the first arrow travel? You may assume that the arrows traveled in straight-line paths and that the bull's eye is circular. Round answer to the nearest tenth.
    1. 19.9 meters
    2. 24 meters
    3. 22 meters
    4. 20.1 meters
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