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8th grade · Math · Unit 16 of 19

Cones, Cylinders & Spheres

Volume of round solids

What your child practices

Using the volume formulas for cylinders, cones and spheres, in terms of π and with 3.14.

New York State Learning Standards learning standard: NY-8.G.9 · using the formulas for the volumes of cones, cylinders and spheres

How we explain it

Children can open this short lesson before they practice.

  1. Cylinder: V = πr²h.
  2. Cone: V = ⅓πr²h, one third of the matching cylinder.
  3. Sphere: V = (4/3)πr³.

Example: A cylinder has radius 3 cm and height 5 cm. What is its volume, in terms of π? r² = 9. 9 × 5 = 45. Answer: 45π cm³

Cones, Cylinders & Spheres in New York

In the New York State Learning Standards, this is unit 16 of 19 in 8th grade Math, after Functions and before Slope & Rate of Change.

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: New York State Education Department (NYSED)

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

    A cone and a cylinder have the same base and height. The cylinder holds 21 cm³. How much does the cone hold?

    • 18 cm³
    • 10.5 cm³
    • 63 cm³
    • 7 cm³

  2. Question 2

    A cone has radius 6 in and height 12 in. What is its volume, in terms of π?

    • 180π in³
    • 432π in³
    • 48π in³
    • 144π in³

  3. Question 3

    A ball has radius 3 cm. What is its volume, in terms of π?

    • 72π cm³
    • 36π cm³
    • 27π cm³

  4. Question 4

    A cylinder has radius 5 cm and height 10 cm. What is its volume, in terms of π?

    • 1000π cm³
    • 50π cm³
    • 250π cm³
    • 100π cm³

  5. Question 5

    A can has radius 4 cm and height 10 cm. Using 3.14 for π, what is its volume in cm³?

    answer boxcm³

  6. Question 6

    A ball has radius 6 cm. What is its volume, in terms of π?

    • 288π cm³
    • 144π cm³
    • 576π cm³
    • 216π cm³

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