Testinar Grade 7 math

Volume of Prisms

Students will build Grade 7 mastery of volume of prisms using models, equations, and test-style reasoning.

CH07-06 Measurement Geometry
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A triangular prism has a triangular base with area \(15\) cm\(^2\) and a height of \(10\) cm. What is its volume?

    1. \(25\) cm\(^3\)
    2. \(75\) cm\(^3\)
    3. \(150\) cm\(^3\)
    4. \(300\) cm\(^3\)

  2. A rectangular prism has dimensions \(5\) m, \(4\) m, and \(8\) m. What is its volume?

    1. \(320\) m\(^3\)
    2. \(160\) m\(^3\)
    3. \(40\) m\(^3\)
    4. \(17\) m\(^3\)

  3. A rectangular prism has a base area of \(24\) square inches and a height of \(6\) inches. Find the volume.

    1. \(288\) in\(^3\)
    2. \(144\) in\(^3\)
    3. \(72\) in\(^3\)
    4. \(30\) in\(^3\)

  4. A rectangular prism has length \(12\) cm, width \(5\) cm, and height \(3\) cm. Which expression correctly represents the volume?

    1. \((12 + 5) \times 3\)
    2. \(12 \times 5 \times 3\)
    3. \(2(12 + 5 + 3)\)
    4. \(12 + 5 + 3\)

  5. The rectangular prism shown has dimensions as labeled. What is its volume in cubic units?

    Volume of Prisms visual for G7-C07-T06-Q005
    1. \(15\) cubic units
    2. \(60\) cubic units
    3. \(120\) cubic units
    4. \(240\) cubic units

  6. A rectangular prism has volume \(240\) cm\(^3\) and base area \(30\) cm\(^2\). What is the height of the prism?

    1. \(8\) cm
    2. \(10\) cm
    3. \(15\) cm
    4. \(210\) cm

  7. A triangular prism has volume \(126\) cubic inches. If the triangular base has area \(18\) in\(^2\), what is the height of the prism?

    1. \(7\) in
    2. \(8\) in
    3. \(9\) in
    4. \(144\) in

  8. Convert \(2\) cubic meters to cubic centimeters. (Hint: \(1\) m \(= 100\) cm)

    1. \(2 \times 10^6\) cm\(^3\)
    2. \(2 \times 10^8\) cm\(^3\)
    3. \(2 \times 10^{12}\) cm\(^3\)
    4. \(2 \times 10^9\) cm\(^3\)
Teacher and parent reference

Answer key and explanations

  1. C. \(150\) cm\(^3\)

    Volume of a prism \(=\) base area \(\times\) height \(=15\times10=150\) cm\(^3\).

  2. B. \(160\) m\(^3\)

    Volume \(= l \times w \times h = 5 \times 4 \times 8 = 160\) m\(^3\).

  3. B. \(144\) in\(^3\)

    \(V = B \times h = 24 \times 6 = 144\) in\(^3\).

  4. B. \(12 \times 5 \times 3\)

    Volume of a rectangular prism is length \(\times\) width \(\times\) height, so \(12 \times 5 \times 3 = 180\) cm\(^3\).

  5. C. \(120\) cubic units

    \(V = 6 \times 4 \times 5 = 120\) cubic units.

  6. A. \(8\) cm

    Rearranging \(V = B \times h\), we get \(h = \frac{V}{B} = \frac{240}{30} = 8\) cm.

  7. A. \(7\) in

    \(h = \frac{V}{B} = \frac{126}{18} = 7\) inches.

  8. A. \(2 \times 10^6\) cm\(^3\)

    \(1\) m \(= 100\) cm, so \(1\) m\(^3 = (100)^3 = 1{,}000{,}000\) cm\(^3 = 10^6\) cm\(^3\). Thus \(2\) m\(^3 = 2 \times 10^6\) cm\(^3\).

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