Worksheet

Volume of combined solids

Grade 10 Math Worksheet - Building Confidence

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Circle the best answer.

  1. Ari's silo is a cylinder 8 m across and 10 m tall, topped by a half-ball. Which expression gives its volume in m³?

    • π·4²·10
    • π·4²·10 + (2/3)π·4³
    • π·4²·10 + (4/3)π·4³
    • π·8²·10 + (2/3)π·8³

  2. Bo's toy rocket is a can 6 in across and 10 in tall with a cone tip 4 in tall. Which expression gives its volume in in³?

    • π·6²·10 + (1/3)π·6²·4 = 408π
    • π·3²·10 = 90π
    • π·3²·10 + (1/3)π·3²·4 = 102π
    • π·3²·10 + π·3²·4 = 126π

  3. A block is 10 cm by 8 cm by 6 cm. Esme drills a round hole 4 cm across straight through the 6 cm height. Which expression gives the volume left?

    • 10·8·6 − π·2²·6 = 480 − 24π
    • 10·8·6 − π·4²·6 = 480 − 96π
    • 10·8·6 + π·2²·6 = 480 + 24π
    • 10·8·6 = 480

  4. Jun's treat is a cone 6 cm across and 9 cm tall with a half-ball scoop of the same width on top. Which expression gives its volume?

    • π·3²·9 + (2/3)π·3³ = 99π
    • (1/3)π·3²·9 + (2/3)π·3³ = 45π
    • (1/3)π·6²·9 + (2/3)π·6³
    • (1/3)π·3²·9 + (4/3)π·3³ = 63π

  5. A pyramid has a square base 6 cm on a side. Each face has slant height 5 cm. Milo finds the volume. What is it?

    • 144 cm³: 36 × 4, no third
    • 60 cm³: height taken as the slant, 5 cm
    • 12 cm³: base area 3 × 3 = 9
    • 48 cm³: height √(5² − 3²) = 4 cm

  6. A cone-shaped pile has a base circumference of 18.84 m and slant height 5 m. Noah finds its volume with π = 3.14. What is it?

    • 113.04 m³: no third
    • 37.68 m³: r = 3 m, height 4 m
    • 3 m: the radius
    • 47.1 m³: height taken as the slant, 5 m

  7. Sketch, not to scale. A straight stack of coins has volume 100 cm³. Pia slides the coins so the stack leans, with the same coins and the same height. What is the volume now?

    • 100 × cos of the lean angle, because the stack tilts
    • Less than 100 cm³: the leaning stack looks smaller
    • More than 100 cm³: the slanted side is longer
    • Still 100 cm³: every layer keeps the same area

  8. Solid A is a box 4 by 3 by 10 cm. Solid B is 10 cm tall with curved sides, and every slice has area 12 cm². Ren compares them. What is true?

    • B is larger: its curved surface is longer than the box's surface
    • Equal, 120 cm³ each, since every slice has the same area
    • A is larger: a box looks bulkier
    • A is 120 cm³, but B cannot be found without its shape

  9. A cone and a pyramid both have base area 30 cm² and height 12 cm. Tala compares their volumes. What is true?

    • Both are 360 cm³: base area times height
    • The cone is larger because its base is round
    • The cone is (1/3)π × 30² × 12 ≈ 11,310 cm³, using the area as the radius
    • They are equal: (1/3) × 30 × 12 = 120 cm³ each

  10. Sketch, not to scale. A sphere has radius 5 cm. A flat cut 3 cm from its center makes a circle. Zee finds the circle's area. What is it?

    • 16π cm²: radius √(5² − 3²) = 4
    • 34π cm²: radius √(5² + 3²)
    • 25π cm²: the sphere's biggest circle
    • 9π cm²: radius 3
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Volume of combined solids

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

  1. Ari's silo is a cylinder 8 m across and 10 m tall, topped by a half-ball. Which expression gives its volume in m³?

    • π·4²·10
    • π·4²·10 + (2/3)π·4³
    • π·4²·10 + (4/3)π·4³
    • π·8²·10 + (2/3)π·8³

  2. Bo's toy rocket is a can 6 in across and 10 in tall with a cone tip 4 in tall. Which expression gives its volume in in³?

    • π·6²·10 + (1/3)π·6²·4 = 408π
    • π·3²·10 = 90π
    • π·3²·10 + (1/3)π·3²·4 = 102π
    • π·3²·10 + π·3²·4 = 126π

  3. A block is 10 cm by 8 cm by 6 cm. Esme drills a round hole 4 cm across straight through the 6 cm height. Which expression gives the volume left?

    • 10·8·6 − π·2²·6 = 480 − 24π
    • 10·8·6 − π·4²·6 = 480 − 96π
    • 10·8·6 + π·2²·6 = 480 + 24π
    • 10·8·6 = 480

  4. Jun's treat is a cone 6 cm across and 9 cm tall with a half-ball scoop of the same width on top. Which expression gives its volume?

    • π·3²·9 + (2/3)π·3³ = 99π
    • (1/3)π·3²·9 + (2/3)π·3³ = 45π
    • (1/3)π·6²·9 + (2/3)π·6³
    • (1/3)π·3²·9 + (4/3)π·3³ = 63π

  5. A pyramid has a square base 6 cm on a side. Each face has slant height 5 cm. Milo finds the volume. What is it?

    • 144 cm³: 36 × 4, no third
    • 60 cm³: height taken as the slant, 5 cm
    • 12 cm³: base area 3 × 3 = 9
    • 48 cm³: height √(5² − 3²) = 4 cm

  6. A cone-shaped pile has a base circumference of 18.84 m and slant height 5 m. Noah finds its volume with π = 3.14. What is it?

    • 113.04 m³: no third
    • 37.68 m³: r = 3 m, height 4 m
    • 3 m: the radius
    • 47.1 m³: height taken as the slant, 5 m

  7. Sketch, not to scale. A straight stack of coins has volume 100 cm³. Pia slides the coins so the stack leans, with the same coins and the same height. What is the volume now?

    • 100 × cos of the lean angle, because the stack tilts
    • Less than 100 cm³: the leaning stack looks smaller
    • More than 100 cm³: the slanted side is longer
    • Still 100 cm³: every layer keeps the same area

  8. Solid A is a box 4 by 3 by 10 cm. Solid B is 10 cm tall with curved sides, and every slice has area 12 cm². Ren compares them. What is true?

    • B is larger: its curved surface is longer than the box's surface
    • Equal, 120 cm³ each, since every slice has the same area
    • A is larger: a box looks bulkier
    • A is 120 cm³, but B cannot be found without its shape

  9. A cone and a pyramid both have base area 30 cm² and height 12 cm. Tala compares their volumes. What is true?

    • Both are 360 cm³: base area times height
    • The cone is larger because its base is round
    • The cone is (1/3)π × 30² × 12 ≈ 11,310 cm³, using the area as the radius
    • They are equal: (1/3) × 30 × 12 = 120 cm³ each

  10. Sketch, not to scale. A sphere has radius 5 cm. A flat cut 3 cm from its center makes a circle. Zee finds the circle's area. What is it?

    • 16π cm²: radius √(5² − 3²) = 4
    • 34π cm²: radius √(5² + 3²)
    • 25π cm²: the sphere's biggest circle
    • 9π cm²: radius 3