Square and cubic units, and density

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ari's mural covers 12 square yards. Paint is priced per square foot (1 yard = 3 feet). Which setup gives the area in square feet?

   • 12 yd² ÷ 9 ft² per yd² ≈ 1.3
   • 12 yd² × 9 ft² per yd² = 108 ft²
   • 12 yd² × 3 ft per yd = 36 ft
   • 12 yd² × 27 ft³ per yd³ = 324 ft²
2. 2.

   A tank holds 2.4 m³ of water. Bo wants the volume in cm³ (1 m = 100 cm). Which setup is right?

   • 2.4 m³ × 1,000,000 cm³ per m³ = 2,400,000 cm³
   • 2.4 m³ × 100 cm per m = 240 cm³
   • 2.4 m³ × 10,000 cm³ per m³ = 24,000 cm³
   • 2.4 m³ ÷ 1,000,000 cm³ per m³ ≈ 0.0000024 cm³
3. 3.

   A pool is 10 m by 5 m and filled 2 m deep. Water is 1 g per cm³. Jun finds the mass in kg. Which setup is right?

   • 100 m³ × 1 g per cm³ = 100 g
   • 100 × 100 × 1 ÷ 1,000 = 10 kg
   • 100 m³ × 1,000,000 cm³ per m³ × 1 g per cm³ ÷ 1,000 g per kg = 100,000 kg
   • 100 × 10,000 × 1 ÷ 1,000 = 1,000 kg
4. 4.

   Kira compares two blocks. Block A is 540 g and 300 cm³. Block B is 0.45 kg and 150 cm³. Which is denser?

   • Block A: its mass is greater, 540 g against 450 g
   • Block B: 450 g ÷ 150 cm³ = 3.0 g/cm³, against A's 1.8
   • Block A: 540 ÷ 300 = 1.8 beats 0.45 ÷ 150 = 0.003
   • Block A: its volume is greater, so it holds more matter
5. 5.

   Luz drops a cylinder into water (1 g/cm³): diameter 4 cm, height 10 cm, mass 400 g. Use π = 3.14. Does it float or sink?

   • It floats: 125.6 ÷ 400 ≈ 0.3 g/cm³
   • It floats: volume 3.14 × 4² × 10 = 502.4 cm³, so 400 ÷ 502.4 ≈ 0.8 g/cm³
   • It sinks: volume 3.14 × 2² × 10 = 125.6 cm³, so 400 ÷ 125.6 ≈ 3.2 g/cm³
   • It floats: 400 g is a light mass
6. 6.

   Balsa wood is 160 kg per m³. Cork is 0.24 g per cm³. Milo asks which is denser. Which answer is right?

   • Balsa: 160 kg/m³ = 1.6 g/cm³, more than 0.24
   • Cork: balsa is 160 kg/m³ = 0.16 g/cm³, less than 0.24
   • Balsa: 160 kg/m³ = 16 g/cm³, more than 0.24
   • Balsa: 160 is already larger than 0.24, so no conversion is needed
7. 7.

   A metal rod has diameter 2 cm, length 20 cm and mass 0.5 kg. Noah finds its density in g/cm³ with π = 3.14. Which is right?

   • 500 ÷ (3.14 × 2² × 20) ≈ 2.0 g/cm³
   • 62.8 ÷ 500 ≈ 0.13 g/cm³
   • 0.5 ÷ 62.8 ≈ 0.008 g/cm³
   • 500 ÷ (3.14 × 1² × 20) ≈ 8.0 g/cm³
8. 8.

   Pia's model car has every length 1/10 of the real car's and is made of the same steel. Which statement about its mass is right?

   • It has 1/1000 of the real mass and 1/1000 of the density
   • It has 1/1000 of the real mass and the same density
   • It has 1/10 of the real mass
   • It has 1/100 of the real mass
9. 9.

   Tala builds a planter 3 times as long, wide and tall as an old one. By what factors do the wood area and the soil volume grow?

   • Wood area × 9, soil volume × 27
   • Wood area × 3, soil volume × 3
   • Wood area × 27, soil volume × 27
   • Wood area × 9, soil volume × 9
10. 10.

    Pia cuts a 1 kg block of cheese (1.1 g/cm³) in half. Zee states each half's mass and density. Which is right?

    • Each half: 0.5 kg and still 1.1 g/cm³
    • Each half: 0.5 kg and 0.55 g/cm³
    • Each half: 0.25 kg and 1.1 g/cm³
    • Each half: 1 kg and 1.1 g/cm³