Modeling with geometry

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. A cylinder of radius 4 is sliced by a plane parallel to its base. What shape is the cross section?
    1. A circle of radius 4
    2. A rectangle
    3. An ellipse
  2. A 9 by 6 rectangle is rotated about one of its sides. Which solid does it sweep out?
    1. A cylinder
    2. A cone
    3. A sphere
  3. A cone of height 3 is sliced by a vertical plane through its apex. What shape is the cross section?
    1. An isosceles triangle
    2. A circle
    3. A rectangle
  4. A solid has volume 25 cm³. It is enlarged with scale factor 2. Find the new volume.
  5. A solid has surface area 49 cm². It is enlarged with scale factor 3. Find the new surface area.
  6. Two similar solids have volumes in the ratio 27:127 : 1. Find the ratio of their heights (scale factor).
  7. Find the volume of a sphere of radius 5 cm (exact, in terms of π).Not to scale
  8. A block has mass 526 g and volume 27 cm³. Find its density (g/cm³).
  9. Find the volume of a hemisphere (half a ball) of radius 3 cm (exact, in terms of π).
  10. How many inches are in 5 feet? (1 foot = 12 inches)
  11. How many meters are 600 centimeters? (1 m = 100 cm)
  12. A rope is 11 yards and 2 feet long. How long is it in feet? (1 yard = 3 feet)