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9th grade · Math · Unit 12 of 18

Volume & Units

Pyramids, cones and conversions

What your child practices

A pyramid holds a third of the matching prism and a cone a third of the matching cylinder, plus converting between metric units and between metric and imperial units.

Alabama Course of Study content standard: GDA.2; GDA.17 · using units to solve problems, and volumes of cones, cylinders, pyramids and prisms

How we explain it

Children can open this short lesson before they practice.

  1. Volume of a pyramid or cone = one third of base area × height.
  2. Convert units by multiplying or dividing by the conversion factor.
  3. Volume units are cubed, so factors are cubed too.

Example: A cone has a base area of 12 cm² and a height of 5 cm. What is its volume? 12 × 5 = 60. 60 ÷ 3 = 20. Answer: 20 cm³

Volume & Units in Alabama

In the Alabama Course of Study, this is unit 12 of 18 in 9th grade Math, after Surface Area of Objects and before Data & Scatter Plots.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alabama State Department of Education (ALSDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    How many 125 mL glasses can be filled from a 4 L jug?

    answer box

  2. Question 2

    A prism and a pyramid have the same base and the same height. The prism's volume is 60 cm³. What is the pyramid's volume, in cm³?

    answer boxcm³

  3. Question 3

    A cone has a radius of 3 cm and a height of 6 cm. Its volume is how many π cm³? (V = 1/3 × π × r² × h)

    answer boxπ cm³

  4. Question 4

    A pyramid has a square base 6 m by 6 m and a height of 3 m. What is its volume, in m³?

    answer boxm³

  5. Question 5

    A cylinder and a cone have the same base and the same height. The cylinder holds 114 cm³. How much does the cone hold, in cm³?

    answer boxcm³

  6. Question 6

    A board is 20 inches long. About how many centimeters is that? (1 inch = 2.54 cm)

    answer boxcm

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