Worksheet

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

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. 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?

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

  2. 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?

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

  3. 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?

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

  4. 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?

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

  5. 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
    • Neither: the same volume means the same metal.
    • Can B, by about 6.3 cm²
    • Can A, by 2 cm²

  6. 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?

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

  7. Pia fills a box-shaped tank, 80 cm by 50 cm by 40 cm, to a depth of 30 cm with a hose giving 12 L a minute. How many minutes does it take?

    • 120 minutes
    • 10 minutes
    • 13.3 minutes
    • 10,000 minutes

  8. Soup cans, each 7 cm across and 12 cm tall, are packed upright in a box 21 cm by 28 cm by 12 cm inside. Ren wants the most cans. How many fit?

    • 15
    • 16
    • 9
    • 12

  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?

    • 16
    • 8
    • 7
    • 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
PencilGopencilgo.com

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

Answer Key - Grade 10 Math Worksheet

Circle the best answer.

  1. 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?

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

  2. 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?

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

  3. 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?

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

  4. 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?

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

  5. 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
    • Neither: the same volume means the same metal.
    • Can B, by about 6.3 cm²
    • Can A, by 2 cm²

  6. 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?

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

  7. Pia fills a box-shaped tank, 80 cm by 50 cm by 40 cm, to a depth of 30 cm with a hose giving 12 L a minute. How many minutes does it take?

    • 120 minutes
    • 10 minutes
    • 13.3 minutes
    • 10,000 minutes

  8. Soup cans, each 7 cm across and 12 cm tall, are packed upright in a box 21 cm by 28 cm by 12 cm inside. Ren wants the most cans. How many fit?

    • 15
    • 16
    • 9
    • 12

  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?

    • 16
    • 8
    • 7
    • 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