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8th grade · Math · Unit 9 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.6(B); 8.7(A) · volume of cylinders, cones 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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 9 of 15 in 8th grade Math, after Scatter Plots & Stories and before Surface Area & Volume.

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: Texas Education Agency (TEA)

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 18 cm³. How much does the cone hold?

    • 15 cm³
    • 9 cm³
    • 6 cm³
    • 54 cm³

  2. Question 2

    A can has radius 5 cm and height 4 cm. Using 3.14 for π, what is its volume in cm³?

    answer boxcm³

  3. Question 3

    A cylinder has radius 6 cm and height 7 cm. What is its volume, in terms of π?

    • 252π cm³
    • 84π cm³
    • 42π cm³
    • 1008π cm³

  4. Question 4

    A ball has radius 9 cm. What is its volume, in terms of π?

    • 972π cm³
    • 729π cm³
    • 324π cm³
    • 1944π cm³

  5. Question 5

    A cone has radius 5 in and height 9 in. What is its volume, in terms of π?

    • 75π in³
    • 225π in³
    • 100π in³
    • 30π in³

  6. Question 6

    A cone has radius 6 in and height 3 in. What is its volume, in terms of π?

    • 36π in³
    • 12π in³
    • 108π in³
    • 72π in³

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