Testinar Grade 8 math

Volume of Pyramids

Learn to reason about and solve Grade 8 problems involving Volume of Pyramids.

CH05-11 Geometry and Measurement
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. The square pyramid below has a base edge of \(8\) cm and a height of \(6\) cm. What is the volume of the pyramid?

    Volume of Pyramids visual for G8-C05-T11-Q006
    1. \(64\) cm\(^3\)
    2. \(128\) cm\(^3\)
    3. \(256\) cm\(^3\)
    4. \(384\) cm\(^3\)

  2. A pyramid with a pentagonal base has a base area of \(25\) cm\(^2\) and a height of \(9\) cm. What is its volume?

    Volume of Pyramids visual for G8-C05-T11-Q034
    1. \(75\) cm\(^3\)
    2. \(225\) cm\(^3\)
    3. \(450\) cm\(^3\)
    4. \(675\) cm\(^3\)

  3. A pyramid has a right-triangular base with legs \(10\) cm and \(6\) cm. The pyramid height is \(15\) cm. What is its volume?

    Volume of Pyramids visual for G8-C05-T11-Q038
    1. \(150\) cm\(^3\)
    2. \(300\) cm\(^3\)
    3. \(450\) cm\(^3\)
    4. \(900\) cm\(^3\)

  4. A pyramid has a rectangular base of \(9\) m by \(4\) m and a height of \(6\) m. What is its volume?

    Volume of Pyramids visual for G8-C05-T11-Q040
    1. \(36\) m\(^3\)
    2. \(72\) m\(^3\)
    3. \(216\) m\(^3\)
    4. \(432\) m\(^3\)

  5. Pyramid X has a square base with side \(8\) cm and height \(10\) cm. Pyramid Y has a rectangular base of \(6\) cm by \(10\) cm and height \(12\) cm. Which pyramid has the larger volume?

    Volume of Pyramids visual for G8-C05-T11-Q042
    1. Pyramid X
    2. Pyramid Y
    3. They have equal volumes.
    4. Cannot be determined.

  6. A rectangular prism with base \(10\) cm by \(8\) cm and height \(6\) cm is topped with a pyramid (same base, height \(3\) cm). What is the total volume?

    Volume of Pyramids visual for G8-C05-T11-Q043
    1. \(480\) cm\(^3\)
    2. \(560\) cm\(^3\)
    3. \(640\) cm\(^3\)
    4. \(800\) cm\(^3\)

  7. A square pyramid has a base edge of \(6\) inches and a height of \(9\) inches. What is its volume?

    1. \(54\) in\(^3\)
    2. \(108\) in\(^3\)
    3. \(162\) in\(^3\)
    4. \(324\) in\(^3\)

  8. A rectangular pyramid has a base that is \(4\) cm by \(5\) cm and a height of \(12\) cm. What is the volume?

    1. \(60\) cm\(^3\)
    2. \(80\) cm\(^3\)
    3. \(240\) cm\(^3\)
    4. \(120\) cm\(^3\)
Teacher and parent reference

Answer key and explanations

  1. B. \(128\) cm\(^3\)

    \(V=\frac{1}{3}\times(8\times8)\times6=\frac{1}{3}\times64\times6=128\) cm\(^3\).

  2. A. \(75\) cm\(^3\)

    \(V=\frac{1}{3}\times25\times9=75\) cm\(^3\).

  3. A. \(150\) cm\(^3\)

    Base area: \(B=\frac{1}{2}\times10\times6=30\) cm\(^2\). Volume: \(V=\frac{1}{3}\times30\times15=150\) cm\(^3\).

  4. B. \(72\) m\(^3\)

    \(B=9\times4=36\) m\(^2\). \(V=\frac{1}{3}\times36\times6=72\) m\(^3\).

  5. B. Pyramid Y

    \(V_X=\frac{1}{3}\times64\times10\approx213.3\) cm\(^3\). \(V_Y=\frac{1}{3}\times60\times12=240\) cm\(^3\). Pyramid Y is larger.

  6. B. \(560\) cm\(^3\)

    Prism volume: \(10\times8\times6=480\) cm\(^3\). Pyramid volume: \(\frac{1}{3}\times(10\times8)\times3=80\) cm\(^3\). Total volume is \(480+80=560\) cm\(^3\).

  7. B. \(108\) in\(^3\)

    Volume of a pyramid: \(V=\frac{1}{3}\cdot B\cdot h=\frac{1}{3}\times(6\times6)\times9=\frac{1}{3}\times36\times9=108\) in\(^3\).

  8. B. \(80\) cm\(^3\)

    \(V=\frac{1}{3}\times B\times h=\frac{1}{3}\times(4\times5)\times12=\frac{1}{3}\times20\times12=80\) cm\(^3\).

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