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

Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

1. Read this first

   Cans holding 1000 cm³ (example figures, made up for practice)

   radius (cm)	height (cm)	metal (cm²)
   3	35.4	723.2
   4	19.9	600.5
   5	12.7	557.1
   5.4	10.9	553.6
   6	8.8	559.5
   7	6.5	593.6

2. 1.

   Ari studies the cans on the card, each holding 1000 cm³. Which statement does the card support best?

   • Taller, narrower cans use less metal, so the r = 3 cm can is the one to choose.
   • The least metal in the table is at r = 5.4 cm, where the height is about the diameter.
   • Metal falls steadily as the radius grows, so each wider can costs less to make.
   • The widest can, r = 7 cm, uses the least metal, because wider cans are shorter.
3. 2.

   Bo makes open boxes by cutting squares from the corners of a 24 cm sheet. Which statement does the card support best?

   • Volume falls as the cut grows larger, so the smallest cut shown, 1 cm, is the one to choose.
   • Volume keeps rising as the cut grows, so the biggest cut shown, 6 cm, is the one to choose.
   • A 4 cm cut gives the most volume possible, because 1024 is the largest value on the card.
   • Of these cuts, 4 cm gives the most volume, 1024 cm³; the card cannot rule out cuts between them.
4. 3.

   Esme's 1:10 scale model of a statue has a mass of 2 kg and needs 50 mL of paint. What do the real statue's mass and paint need?

   • 200 kg and 5 L
   • 2,000 kg and 500 mL
   • 2,000 kg and 5 L
   • 20 kg and 500 mL
5. 4.

   Gravel pours at 3 m³ a minute into a cone-shaped pile whose height equals its radius. After 10 minutes, about how wide is Jun's pile's radius? Use π = 3.14.

   • About 3.1 m
   • About 2.4 m
   • About 28.6 m
   • About 2.1 m
6. 5.

   A steel pipe has outer diameter 10 cm, wall thickness 0.5 cm and length 2 m. Steel has a density of 7.85 g/cm³. Using π = 3.14, about how heavy is Kira's pipe?

   • About 93.7 kg
   • About 0.23 kg
   • About 123.2 kg
   • About 23.4 kg

7. Two cans of the same volume (example figures, made up for practice)

   can	side area (cm²)	end area (cm²)
   A	251.2	100.5
   B	201.0	157.0

8. 6.

   Luz compares the two cans on the card. Side metal costs $0.002 per cm² and end metal costs $0.004 per cm². Which can costs less, and by how much?

   • Can B, by about $0.13
   • Can A, by about $0.01
   • Can B, by about $0.09
   • Can A, by about $0.13
9. 7.

   A tree trunk is 10 m tall, 40 cm across at the base and 30 cm across at the top. Milo uses π = 3.14. Which statement about the trunk's volume is best supported?

   • It is about 1.26 m³, since the trunk is 40 cm across at its widest point, the base.
   • It is exactly 0.98 m³, the average of the two cylinder volumes at 30 cm and 40 cm.
   • It is about 0.71 m³, since the trunk is just 30 cm across at its narrowest point, the top.
   • It is between about 0.71 m³ and 1.26 m³; a tapered model gives about 0.97 m³.
10. 8.

    Noah fences a 200 m² rectangular garden. The street side costs $8 per meter and the other three sides cost $5 per meter. Which of these sizes costs least?

    • 16 m street side by 12.5 m: about $333.00
    • 10 m street side by 20 m: about $330.00
    • 12 m street side by 16.7 m: about $322.67
    • 14.1 m street side by 14.1 m: about $325.27
11. 9.

    A ball of radius r fits snugly inside Ren's cylinder, touching the sides, top and bottom. What fraction of the cylinder's volume does the ball fill?

    • 1/2
    • 2/3
    • π/6, about 0.52
    • 3/2
12. 10.

    Zee says doubling every dimension of a box doubles both the cardboard needed and the volume. Which verdict is right?

    • Yes: both double, since each length doubles.
    • No: the cardboard becomes 4 times as much and the volume 8 times as much.
    • No: the cardboard becomes 8 times as much and the volume 4 times as much.
    • No: the cardboard doubles but the volume becomes 8 times as much.