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GMAT Practice Questions - Solid Geometry

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You are likely to get one to three questions from Solid Geometry in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include finding the area, perimeter of two dimensional geometric shapes and surface area, volume, longest diagnal of solids including cones, cylinders, cube, rectangular cube, sphere, and hemisphere. A collection of GMAT practice questions from Mensuration and Solid Geometry is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

  1. A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

    1. 9
    2. 61
    3. 98
    4. 54
    5. 64
    • Correct AnswerChoice (D).
      54 1 cc cubes will have exactly one of their sides painted.
      Correct answer
    • Explanatory Answer
    • Cubes
    • Medium
  2. A wheel of a car of radius 21 cms is rotating at 600 RPM. What is the speed of the car in km/hr?

    1. 79.2 km/hr
    2. 47.52 km/hr
    3. 7.92 km/hr
    4. 39.6 km/hr
    5. 3.96 km/hr
    • Correct AnswerChoice (B).
      The speed of the car is 47.52 km/hr.
      Correct answer
    • Explanatory Answer
    • Cylinders
    • Medium
  3. The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

    1. 3 minutes
    2. 0.04 hours
    3. 2 minutes
    4. 2.4 minutes
    5. 2 minutes 40 seconds
    • Correct AnswerChoice (C).
      The lady will take 2 minutes to cross the filed diagonally.
      Correct answer
    • Explanatory Answer
    • Diagonals of Squares
    • Easy
  4. A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 211 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?

    1. 11236
    2. 11025
    3. 14400
    4. 12696
    5. Cannot be determined
    • Correct AnswerChoice (A).
      She produced 11236 cabbages this year.
      Correct answer
    • Explanatory Answer
    • Squares
    • Medium
  5. The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}\\) in your calculations.

    1. 1696 sq m
    2. 1694 sq m
    3. 1594 sq m
    4. 1756 sq.m
    5. 1896 sq.m
    • Correct AnswerChoice (B).
      The cow will be able to graze an additional 1694 sq m.
      Correct answer
    • Explanatory Answer
    • Squares and arcs
    • Medium
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