Worksheet

Volume of combined solids

Grade 10 Math Worksheet - Challenge Me

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Circle the best answer.

  1. Silo A is a cylinder of radius 4 m and height 12 m. Silo B holds the same grain but has radius 6 m. Ari finds B's height. What is it?

    • 8 m: radius 4 to 6 scaled the height by 2/3
    • 27 m: height × (6/4)²
    • 12 m: the heights are equal
    • 5⅓ m: 16 × 12 = 36 × h

  2. A can of radius 4 cm and height 10 cm sits in a box 8 cm by 8 cm by 10 cm. Bo finds the share of the box the can fills. What is it?

    • 100%: the can touches the four walls
    • About 26%: the can taken as a cone
    • About 78.5%: 160π ÷ 640 = π/4
    • About 50%: half the box

  3. A ball of radius r fits snugly inside a cylinder of radius r and height 2r. Esme finds the share of the cylinder the ball fills. What is it?

    • 1/2: the ball looks like half
    • π/4: the ratio of a circle to its square
    • 2/3: (4/3)πr³ ÷ 2πr³
    • 1/3: the ball taken as a cone

  4. A cone and a half-ball both have radius r, and the cone is r tall. Jun compares their volumes. What is the ratio of cone to half-ball?

    • 1 to 4: a full ball used
    • 1 to 2: (1/3)πr³ and (2/3)πr³
    • 3 to 2: the cone taken as πr³
    • 1 to 1: both fit in the same cylinder

  5. Two cones are similar. Their heights are 6 cm and 9 cm, and the small one holds 40 mL. Kira finds the big one's capacity. What is it?

    • 90 mL: 40 × (9/6)²
    • 11.9 mL: 40 × (6/9)³
    • 60 mL: 40 × 9/6
    • 135 mL: 40 × (9/6)³

  6. Two bottles are similar; the big one is 1.5 times as tall. Milo compares their label areas and capacities. By what factors do they grow?

    • Label area × 1.5, capacity × 1.5
    • Label area × 2.25, capacity × 3.375
    • Label area × 2.25, capacity × 2.25
    • Label area × 3.375, capacity × 2.25

  7. Sketch, not to scale. A cone-shaped cup is filled with water to half its height. Noah finds the share of the cup's volume that is water. What is it?

    • 1/4: half the radius squared
    • 1/2: half the height, so half the volume
    • 1/8: a similar cone, half as tall
    • 7/8: the empty top compared

  8. A right triangle with legs 3 and 4 spins around one of its legs. Pia picks the spin that makes the bigger cone. Which is it?

    • Spin about the 3 leg: (1/3)π·4²·3 = 16π against 12π
    • Equal: it is the same triangle both times
    • Spin about the hypotenuse 5: the longest side gives the biggest cone
    • Spin about the 4 leg: radius 4 and height 3 give 16π against 12π

  9. A 3 cm by 5 cm rectangle spins around one of its sides to make a can. Ren picks the spin that makes the bigger can. Which is it?

    • Spin about the 5 cm side: the taller can holds more
    • Equal: it is the same rectangle both times
    • Spin about the 3 cm side: π·5²·3 = 75π against 45π
    • Spin about the 5 cm side: π·5²·3 = 75π against 45π

  10. Sketch, not to scale. A can has radius 6 cm and height 6 cm. Zee drills out a cone with the same radius and height. What is left, compared with a half-ball of radius 6 cm?

    • 144π cm³, equal to the half-ball's (2/3)π·6³
    • 0 cm³: the cone taken as π·6²·6
    • 216π cm³: the cone left in
    • 288π cm³: the half-ball taken as a full ball
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Volume of combined solids

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

  1. Silo A is a cylinder of radius 4 m and height 12 m. Silo B holds the same grain but has radius 6 m. Ari finds B's height. What is it?

    • 8 m: radius 4 to 6 scaled the height by 2/3
    • 27 m: height × (6/4)²
    • 12 m: the heights are equal
    • 5⅓ m: 16 × 12 = 36 × h

  2. A can of radius 4 cm and height 10 cm sits in a box 8 cm by 8 cm by 10 cm. Bo finds the share of the box the can fills. What is it?

    • 100%: the can touches the four walls
    • About 26%: the can taken as a cone
    • About 78.5%: 160π ÷ 640 = π/4
    • About 50%: half the box

  3. A ball of radius r fits snugly inside a cylinder of radius r and height 2r. Esme finds the share of the cylinder the ball fills. What is it?

    • 1/2: the ball looks like half
    • π/4: the ratio of a circle to its square
    • 2/3: (4/3)πr³ ÷ 2πr³
    • 1/3: the ball taken as a cone

  4. A cone and a half-ball both have radius r, and the cone is r tall. Jun compares their volumes. What is the ratio of cone to half-ball?

    • 1 to 4: a full ball used
    • 1 to 2: (1/3)πr³ and (2/3)πr³
    • 3 to 2: the cone taken as πr³
    • 1 to 1: both fit in the same cylinder

  5. Two cones are similar. Their heights are 6 cm and 9 cm, and the small one holds 40 mL. Kira finds the big one's capacity. What is it?

    • 90 mL: 40 × (9/6)²
    • 11.9 mL: 40 × (6/9)³
    • 60 mL: 40 × 9/6
    • 135 mL: 40 × (9/6)³

  6. Two bottles are similar; the big one is 1.5 times as tall. Milo compares their label areas and capacities. By what factors do they grow?

    • Label area × 1.5, capacity × 1.5
    • Label area × 2.25, capacity × 3.375
    • Label area × 2.25, capacity × 2.25
    • Label area × 3.375, capacity × 2.25

  7. Sketch, not to scale. A cone-shaped cup is filled with water to half its height. Noah finds the share of the cup's volume that is water. What is it?

    • 1/4: half the radius squared
    • 1/2: half the height, so half the volume
    • 1/8: a similar cone, half as tall
    • 7/8: the empty top compared

  8. A right triangle with legs 3 and 4 spins around one of its legs. Pia picks the spin that makes the bigger cone. Which is it?

    • Spin about the 3 leg: (1/3)π·4²·3 = 16π against 12π
    • Equal: it is the same triangle both times
    • Spin about the hypotenuse 5: the longest side gives the biggest cone
    • Spin about the 4 leg: radius 4 and height 3 give 16π against 12π

  9. A 3 cm by 5 cm rectangle spins around one of its sides to make a can. Ren picks the spin that makes the bigger can. Which is it?

    • Spin about the 5 cm side: the taller can holds more
    • Equal: it is the same rectangle both times
    • Spin about the 3 cm side: π·5²·3 = 75π against 45π
    • Spin about the 5 cm side: π·5²·3 = 75π against 45π

  10. Sketch, not to scale. A can has radius 6 cm and height 6 cm. Zee drills out a cone with the same radius and height. What is left, compared with a half-ball of radius 6 cm?

    • 144π cm³, equal to the half-ball's (2/3)π·6³
    • 0 cm³: the cone taken as π·6²·6
    • 216π cm³: the cone left in
    • 288π cm³: the half-ball taken as a full ball