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Volume Word Problems Practice Questions (page 2)

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Updated on Oct 4, 2011

Practice 2

Problems

  1. What is the volume of a cylinder with a base radius of 2 in. and a height of 4 in.?
  2. What is the volume of a cone with a base radius of 5 m and a height of 6 m?
  3. What is the volume of a sphere with a radius of 9 cm?

Solutions

  1. Read and understand the question. This question is looking for the volume of a cylinder when the radius of the base and the height are known.
  2. Make a plan. Substitute into the volume formula, and then evaluate to find the volume.

    Carry out the plan. The formula becomes V = π(2)2(4). Evaluate the exponent to get V = 4(4)π. Multiply to simplify. The volume is 16π in.3.

    Check your answer. To check this solution, use the strategy of working backward and divide the volume by the height times π. Then, take the positive square root to see if this result is the radius of the base. 16π ÷ 4π = 4. The positive square root of 4 is 2, which is the radius of the base. This answer is checking.

  3. Read and understand the question. This question is asking for the volume of a cone when the radius of the base and the height are given.
  4. Make a plan. Use the formula V = πr2h and substitute the given values.

    Evaluate the formula to find the volume.

    Carry out the plan. The formula becomes V = π(5)2(6). Evaluate the exponent to simplify to V = (25)(6)π. Multiply: V = (150)π. Divide 150 by 3 to simplify: V = 50π m3.

    Check your answer. To check this answer, work backward by multiplying the volume by 3. Then, divide by the height times π and take the positive square root of the result to get the length of the base radius.

      50π × 3 = 150π
      150π ÷ 6π = 25

    The positive square root of 25 is 5, so this question is checking.

  5. Read and understand the question. This question is looking for the volume of a sphere when the radius is given.
  6. Make a plan. Substitute the value of r into the formula and evaluate to find the volume.

    Carry out the plan. The formula becomes V = π(9)3. Evaluate the exponen to get V = π(729). Multiply to get V = 972π cm3.

    Check your answer. To check this result, divide the volume by π. Then, see if the result is the same as 93.

      972π ÷ π = 729

    93 is also equal to 729, so this result is checking.

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