Math by First Principles
Level 1 · Foundational ← Back to lesson

Volumes of Pyramids and Cones: Practice

12 multiple-choice questions, progressively harder.

Level 1 · Foundational 0 / 12 answered
Question 1 of 12
  1. 1

    A pyramid has base area 2424 square cm and perpendicular height 77 cm. Find its volume.

    Dimensions of a pyramidA pyramid with base information 24 cm² and perpendicular height 7 cm. A right-angle mark identifies the height to the base plane. Dashed short edges are hidden; the long-dashed segment is the interior height. The apex need not lie over the base center.7 cm24 cm²
  2. 2

    A pyramid has a square base of side 55 cm and perpendicular height 99 cm. What is its volume?

    Dimensions of a pyramidA pyramid with base information square side 5 cm and perpendicular height 9 cm. A right-angle mark identifies the height to the base plane. Dashed short edges are hidden; the long-dashed segment is the interior height. The apex need not lie over the base center.9 cmsquare side 5 cm
  3. 3

    A circular cone has radius 44 cm and perpendicular height 66 cm. Give its exact volume.

    Dimensions of a coneA right circular cone with base radius 4 cm, perpendicular height 6 cm. The radius meets the height at a marked right angle. The rear half of the base circle and the interior height are dashed. The circular base appears elliptical only because of perspective.6 cm4 cm
  4. 4

    A circular cone has base diameter 1010 cm and perpendicular height 33 cm. What is its exact volume?

    Dimensions of a coneA right circular cone with base radius r, perpendicular height 3 cm. The radius meets the height at a marked right angle. The rear half of the base circle and the interior height are dashed. The circular base appears elliptical only because of perspective.3 cmr
  5. 5

    A pyramid has volume 4242 cubic cm and base area 1818 square cm. Find its perpendicular height.

  6. 6

    A cone has volume 48π48\pi cubic cm and perpendicular height 99 cm. Find its positive radius.

  7. 7

    Which measurement is the height in the volume formula for a pyramid?

  8. 8

    An oblique pyramid has base area 3535 square cm, perpendicular height 66 cm, and a slanted edge of 1010 cm. Find its volume.

    Dimensions of a pyramidA pyramid with base information 35 cm² and perpendicular height 6 cm. A right-angle mark identifies the height to the base plane. Dashed short edges are hidden; the long-dashed segment is the interior height. The apex need not lie over the base center.6 cm35 cm²
  9. 9

    A pyramid has base area 6464 square units. A plane parallel to its base passes halfway from the apex to the base plane. What is its section area?

    A parallel section at a specified levelAn axial triangle shows a pyramid with base area 64 square units. A highlighted segment marks a plane section parallel to the base, halfway below the apex. The section area is unknown.base area 64full perpendicular heightsection area unknownhalf the height below apex
  10. 10

    A cone and a cylinder have the same circular base and the same perpendicular height. What is the ratio of cone volume to cylinder volume?

  11. 11

    A pyramid has a right triangular base with legs 88 cm and 33 cm. Its perpendicular height is 1010 cm. Find its volume.

    A right triangular baseA right triangular base has perpendicular legs 8 cm and 3 cm. The right-angle mark is between those two legs. This is a true view of the base, not a perspective drawing of the entire pyramid.8 cm3 cm
  12. 12

    A cone calculation multiplies a base area in square centimeters by a perpendicular height in centimeters and divides by three. Which unit belongs to its volume?

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