GRE® Geometry Practice

Geometry and Solid Geometry Practice for GRE Quant

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Concepts Tested from Geometry in GRE

Properties of lines, rays, line sgement, parallel lines, angles, angle between intersecting lines, polygons, sum of interior angles of polygons, number of diagonals in a polygon, convex and concave polygons. properties of triangles, median, altitude, perpendicular bisector, angle bisector, circles, chords, tangent, quadrilaterals, tangent secant theorem, inscribed circle and circumscribing circles.

Concepts Tested in Mensuration

Area of triangles, circles, quadrilaterals (including parallelogram, rhombus, rectangle, square, trapezium, and kite) and regular hexagon, surface area and volume of cube, cylinder, cone, sphere and hemisphere, length of the longest diagonal in a cube and cuboid (rectangular cube), volume of water displaced in a vessel when another object is dropped into it, and volume of 3D objects formed by rotation of 2D objects.
A relatively easy topic. Key to success in this topic is to remember all the formulae.

  1. The area for which of the following will be more than 50 square units

    1. Circle whose circumference is 22 units.
    2. Parallelogram whose adjacent sides measure 20 units and 10 units.
    3. Rhombus whose perimeter is 52 units.
    4. Rectangle whose perimeter is 50 units.
    5. Square whose perimeter is 32 units.
    6. Right triangle whose hypotenuse measures 17 units.
  2. A sector of a circle of radius 5 cm is recast into a right circular cone of height 4 cm. What is the volume of the resulting cone?

    1. 12 π cm3
    2. 100 π cm3
    3. 33 π cm3
    4. 32 π cm3
    5. 4 π cm3
  3. A cylindrical vessel is filled with water up to some height. If a sphere of diameter 8 cm is dropped into the cylinder, the water level rises by half of the initial level. Instead, if a second sphere of diameter 16 cm is dropped, the water level rises to a height h2. What percentage of this new height h2 is the initial level of water?

    1. 33⅓%
    2. 40%
    3. 20%
    4. 25%
    5. 16⅙%
  4. Chord AC at a distance of 7 cm from the center of a circle subtends an angle of 120 degrees at the center. What is the area of major segment?

    1. 410⅓ + 7√3 cm2
    2. 410⅔ + 49√3 cm2
    3. 1232 + 49√3 cm2
    4. 1232 + 7√3 cm2
    5. 410⅔ + 49√3 cm2

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