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

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ari models a slightly tapered tree trunk as a cylinder, using the width at the bottom. Compared with the real trunk, the estimate is...

   • Exactly right: both are round, so the cylinder and the trunk have the same volume.
   • Impossible to say, because the trunk's height is not given in the question.
   • Too large: the cylinder is as wide as the base all the way up.
   • Too small: a cylinder holds less than a tapered shape does, so the estimate falls short.
2. 2.

   Bo models an apple as a sphere using its widest width. The apple is a bit squashed, shorter than it is wide. The estimate is...

   • Too large: the sphere is as tall as it is wide, but the apple is not.
   • Exactly right: apples are round, so a sphere fits.
   • Impossible to say without the apple's mass.
   • Too small: a sphere's widest part is its smallest size.
3. 3.

   Esme models a flower pot, wider at the top than at the bottom, as a cylinder using the bottom width. The estimate is...

   • Too large: a cylinder holds more than a flared shape, so the estimate is too big.
   • Impossible to say, because the pot's height is not given in the question.
   • Exactly right: the bottom width is the pot's width, so the cylinder fits the pot.
   • Too small: the cylinder is narrower than the pot everywhere above the bottom.
4. 4.

   Jun's rain barrel is a cylinder 60 cm across and 90 cm tall. Using π = 3.14, about how many liters does it hold?

   • 254 liters
   • 254,340 liters
   • 25.4 liters
   • 1,017 liters
5. 5.

   Kira's juice can is a cylinder 7 cm across and 12 cm tall. Using π = 3.14, about how many milliliters does it hold? (1 cm³ = 1 mL)

   • 1,846 mL
   • 0.46 mL
   • 132 mL
   • 462 mL
6. 6.

   Luz's sandbox is 2 m long, 1.5 m wide and filled 30 cm deep with sand. How many liters of sand is that? (1 m³ = 1,000 liters)

   • 0.9 liters
   • 9,000 liters
   • 90 liters
   • 900 liters
7. 7.

   Milo has 30 m of fence for a rectangular pen. One side is 8 m. What is the pen's area?

   • 176 m²
   • 120 m²
   • 7 m²
   • 56 m²
8. 8.

   Noah fences three sides of a pen with 50 m of fence, using a wall for the fourth side. The two ends are 10 m each. What is the pen's area?

   • 300 m²
   • 30 m²
   • 500 m²
   • 400 m²
9. 9.

   A rope around the edge of Pia's round pool is 31.4 m long. Using π = 3.14, what is the pool's area?

   • 15.7 m²
   • 5 m²
   • 314 m²
   • 78.5 m²
10. 10.

    Ren's closed cardboard box is 10 cm by 6 cm by 4 cm. Cardboard costs $0.004 per cm². What is the cost of the cardboard?

    • $0.96
    • $0.75
    • $0.99
    • $0.50