Testinar Grade 7 math

Cylinder Surface Area and Volume

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

CH07-07 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 cylinder has a radius of \(3\) m and a height of \(5\) m. What is its volume? Use \(\pi\approx3.14\).

    1. \(47.1\) m\(^3\)
    2. \(94.2\) m\(^3\)
    3. \(141.3\) m\(^3\)
    4. \(235.5\) m\(^3\)

  2. A soup can has a radius of \(2\) inches and a height of \(4\) inches. What is the volume of the can? Use \(\pi\approx3.14\).

    1. \(25.12\) in\(^3\)
    2. \(50.24\) in\(^3\)
    3. \(75.36\) in\(^3\)
    4. \(100.48\) in\(^3\)

  3. What is the volume of the cylinder shown? Use \(\pi\approx3.14\).

    Cylinder Surface Area and Volume visual for G7-C07-T07-Q003
    1. \(37.68\) cm\(^3\)
    2. \(50.24\) cm\(^3\)
    3. \(75.36\) cm\(^3\)
    4. \(150.72\) cm\(^3\)

  4. A water tank in the shape of a cylinder has a radius of \(4\) feet and a height of \(10\) feet. Find the volume. Use \(\pi\approx3.14\).

    1. \(125.6\) ft\(^3\)
    2. \(251.2\) ft\(^3\)
    3. \(502.4\) ft\(^3\)
    4. \(1004.8\) ft\(^3\)

  5. A cylindrical drum has a radius of \(1.5\) m and a height of \(2\) m. What is its volume? Use \(\pi\approx3.14\).

    1. \(9.42\) m\(^3\)
    2. \(14.13\) m\(^3\)
    3. \(18.84\) m\(^3\)
    4. \(37.68\) m\(^3\)

  6. Which formula gives the volume of the cylinder shown?

    Cylinder Surface Area and Volume visual for G7-C07-T07-Q006
    1. \(\pi \times 3 \times 7\)
    2. \(\pi \times 3^2 \times 7\)
    3. \(2\pi \times 3 \times 7\)
    4. \(2\pi \times 3^2 \times 7\)

  7. A cylindrical pasta jar has a radius of \(5\) cm and a height of \(15\) cm. What is the surface area of the jar (including both circular ends)? Use \(\pi\approx3.14\).

    1. \(471\) cm\(^2\)
    2. \(628\) cm\(^2\)
    3. \(785\) cm\(^2\)
    4. \(1256\) cm\(^2\)

  8. Find the lateral surface area (curved side only) of the cylinder shown. Use \(\pi\approx3.14\).

    Cylinder Surface Area and Volume visual for G7-C07-T07-Q009
    1. \(39.25\) m\(^2\)
    2. \(62.8\) m\(^2\)
    3. \(125.6\) m\(^2\)
    4. \(188.4\) m\(^2\)
Teacher and parent reference

Answer key and explanations

  1. C. \(141.3\) m\(^3\)

    Volume of a cylinder \(=\pi r^2 h\approx3.14\times3^2\times5=3.14\times9\times5=141.3\) m\(^3\).

  2. B. \(50.24\) in\(^3\)

    \(V = \pi r^2 h \approx 3.14 \times 2^2 \times 4 = 3.14 \times 4 \times 4 = 50.24\) in\(^3\).

  3. C. \(75.36\) cm\(^3\)

    \(V = \pi r^2 h \approx 3.14 \times 2^2 \times 6 = 3.14 \times 4 \times 6 = 75.36\) cm\(^3\).

  4. C. \(502.4\) ft\(^3\)

    \(V = \pi r^2 h \approx 3.14 \times 4^2 \times 10 = 3.14 \times 16 \times 10 = 502.4\) ft\(^3\).

  5. B. \(14.13\) m\(^3\)

    \(V = \pi r^2 h \approx 3.14 \times 1.5^2 \times 2 = 3.14 \times 2.25 \times 2 = 14.13\) m\(^3\).

  6. B. \(\pi \times 3^2 \times 7\)

    The volume formula is \(V = \pi r^2 h\). With \(r=3\) and \(h=7\), this is \(\pi \times 3^2 \times 7\).

  7. B. \(628\) cm\(^2\)

    \(SA = 2\pi r^2 + 2\pi rh = 2(3.14)(5^2) + 2(3.14)(5)(15) = 157 + 471 = 628\) cm\(^2\).

  8. C. \(125.6\) m\(^2\)

    Lateral area \(= 2\pi rh \approx 2 \times 3.14 \times 2.5 \times 8 = 125.6\) m\(^2\).

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