Three-dimensional figures have both enclosed volume and exposed surface area. A reliable solution starts by deciding which quantity is requested and whether the solid is closed.

A reliable method

  1. Identify one edge length.
  2. Multiply the edge by itself three times.
  3. Keep measurements in one unit.
  4. Report cubic units.

Example 1

Find the volume of a cube of edge length \(3\). All lengths use the same unit. Keep pi exact when it occurs.

  1. Use \(V=s^3\).
  2. Substitute the given values: \(3^{3}\).
  3. Calculate without premature rounding: \(27\) cubic units.
  4. Check that the units and the size of the result match the quantity requested.

Answer: \(27\) cubic units

Example 2

Find the volume of a cube of edge length \(5\). All lengths use the same unit. Keep pi exact when it occurs.

  1. Use \(V=s^3\).
  2. Substitute the given values: \(5^{3}\).
  3. Calculate without premature rounding: \(125\) cubic units.
  4. Check that the units and the size of the result match the quantity requested.

Answer: \(125\) cubic units

Common mistakes

  • Volume is not the surface area.
  • Doubling an edge multiplies volume by 8, not 2.

Practice without the answer first

  1. Find the volume of a cube of edge length \(\frac{3}{2}\). All lengths use the same unit. Keep pi exact when it occurs.
  2. Find the volume of a cube of edge length \(8\). All lengths use the same unit. Keep pi exact when it occurs.
  3. Find the volume of a cube of edge length \(10\). All lengths use the same unit. Keep pi exact when it occurs.
Answers and step-by-step explanations

Practice 1

  1. Use \(V=s^3\).
  2. Substitute the given values: \(\left(\frac{3}{2}\right)^{3}\).
  3. Calculate without premature rounding: \(\frac{27}{8}\) cubic units.
  4. Check that the units and the size of the result match the quantity requested.

Answer: \(\frac{27}{8}\) cubic units

Practice 2

  1. Use \(V=s^3\).
  2. Substitute the given values: \(8^{3}\).
  3. Calculate without premature rounding: \(512\) cubic units.
  4. Check that the units and the size of the result match the quantity requested.

Answer: \(512\) cubic units

Practice 3

  1. Use \(V=s^3\).
  2. Substitute the given values: \(10^{3}\).
  3. Calculate without premature rounding: \(1000\) cubic units.
  4. Check that the units and the size of the result match the quantity requested.

Answer: \(1000\) cubic units

These original skill exercises are not official exam questions or a score prediction. Use the coverage notes on your exam hub to choose relevant practice.