Worksheet

Model a real object with a shape, and design problems with limits

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. Ari's grain silo is a cylinder (radius 3 m, wall height 8 m) topped by a hemisphere. Using π = 3.14, what is its volume?

    • 254.3 m³
    • 226.1 m³
    • 339.1 m³
    • 282.6 m³

  2. Bo's ice cream is a cone (radius 3 cm, height 10 cm) topped by a hemisphere scoop of radius 3 cm. Using π = 3.14, what is the total volume?

    • 339.1 cm³
    • 94.2 cm³
    • 207.2 cm³
    • 150.7 cm³

  3. A 1:50 scale model of Esme's school hall has a floor area of 0.2 m². What is the real hall's floor area?

    • 10 m²
    • 250 m²
    • 25,000 m²
    • 500 m²

  4. Jun has 60 m of fence for a rectangular pen. A river forms one side, so only three sides need fence. Which design uses the fence well and gives the most room?

    • 20 m wide, 20 m along the river: 400 m²
    • 15 m wide, 30 m along the river: 450 m²
    • 15 m wide, 15 m along the river: 225 m²
    • 30 m wide, 15 m along the river: 450 m²

  5. Kira cuts a 3 cm square from each corner of a 20 cm square sheet and folds up the sides into an open box. What is the box's volume?

    • 588 cm³
    • 867 cm³
    • 196 cm³
    • 1,200 cm³

  6. Can A (radius 4 cm, height 10 cm) and Can B (radius 5 cm, height 6.4 cm) both hold 160π cm³. Which uses less metal for Luz, and by how much? Use total surface.

    • Can A, by about 6.3 cm²
    • Can B, by about 6.3 cm²
    • Can A, by 2 cm²
    • Neither: the same volume means the same metal.

  7. A 1:20 scale model of Milo's water tank holds 5 L. How many liters does the real tank hold?

    • 40,000 L
    • 100 L
    • 2,000 L
    • 8,000 L

  8. Noah's solid oak cylinder has radius 5 cm, height 20 cm and mass 1,100 g. Using π = 3.14, will it float in water (1 g/cm³), and what is its density?

    • No: about 1.43 g/cm³
    • Yes: about 0.70 g/cm³
    • Yes: about 0.18 g/cm³
    • Yes: about 0.0007 g/cm³

  9. Tala paints the curved side of a round tower, 6 m across and 18 m tall. One liter covers 9 m²; cans hold 5 L. Using π = 3.14, how many cans are needed?

    • 7
    • 8
    • 16
    • 38

  10. Zee's tent is a square pyramid with a 4 m square base and a height of 3 m. The fabric covers the four sloping faces only. How much fabric is needed?

    • About 28.8 m²
    • 57.7 m²
    • 24 m²
    • 44.8 m²
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Model a real object with a shape, and design problems with limits

Answer Key - Grade 10 Math Worksheet

Circle the best answer.

  1. Ari's grain silo is a cylinder (radius 3 m, wall height 8 m) topped by a hemisphere. Using π = 3.14, what is its volume?

    • 254.3 m³
    • 226.1 m³
    • 339.1 m³
    • 282.6 m³

  2. Bo's ice cream is a cone (radius 3 cm, height 10 cm) topped by a hemisphere scoop of radius 3 cm. Using π = 3.14, what is the total volume?

    • 339.1 cm³
    • 94.2 cm³
    • 207.2 cm³
    • 150.7 cm³

  3. A 1:50 scale model of Esme's school hall has a floor area of 0.2 m². What is the real hall's floor area?

    • 10 m²
    • 250 m²
    • 25,000 m²
    • 500 m²

  4. Jun has 60 m of fence for a rectangular pen. A river forms one side, so only three sides need fence. Which design uses the fence well and gives the most room?

    • 20 m wide, 20 m along the river: 400 m²
    • 15 m wide, 30 m along the river: 450 m²
    • 15 m wide, 15 m along the river: 225 m²
    • 30 m wide, 15 m along the river: 450 m²

  5. Kira cuts a 3 cm square from each corner of a 20 cm square sheet and folds up the sides into an open box. What is the box's volume?

    • 588 cm³
    • 867 cm³
    • 196 cm³
    • 1,200 cm³

  6. Can A (radius 4 cm, height 10 cm) and Can B (radius 5 cm, height 6.4 cm) both hold 160π cm³. Which uses less metal for Luz, and by how much? Use total surface.

    • Can A, by about 6.3 cm²
    • Can B, by about 6.3 cm²
    • Can A, by 2 cm²
    • Neither: the same volume means the same metal.

  7. A 1:20 scale model of Milo's water tank holds 5 L. How many liters does the real tank hold?

    • 40,000 L
    • 100 L
    • 2,000 L
    • 8,000 L

  8. Noah's solid oak cylinder has radius 5 cm, height 20 cm and mass 1,100 g. Using π = 3.14, will it float in water (1 g/cm³), and what is its density?

    • No: about 1.43 g/cm³
    • Yes: about 0.70 g/cm³
    • Yes: about 0.18 g/cm³
    • Yes: about 0.0007 g/cm³

  9. Tala paints the curved side of a round tower, 6 m across and 18 m tall. One liter covers 9 m²; cans hold 5 L. Using π = 3.14, how many cans are needed?

    • 7
    • 8
    • 16
    • 38

  10. Zee's tent is a square pyramid with a 4 m square base and a height of 3 m. The fabric covers the four sloping faces only. How much fabric is needed?

    • About 28.8 m²
    • 57.7 m²
    • 24 m²
    • 44.8 m²