Square and cubic units, and density
Grade 10 Math Worksheet - Building Confidence
Circle the best answer.
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 = 108 ft²
- 12 yd² × 3 ft per yd = 36 ft
- 12 yd² × 27 ft³ per yd³ = 324 ft²
- 12 yd² ÷ 9 ft² per yd² ≈ 1.3
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 ≈ 0.0000024 cm³
- 2.4 m³ × 1,000,000 cm³ per m³ = 2,400,000 cm³
- 2.4 m³ × 10,000 cm³ per m³ = 24,000 cm³
- 2.4 m³ × 100 cm per m = 240 cm³
A sandbox is 3 m by 2 m and 40 cm deep. Sand weighs 1,600 kg per m³. Esme finds its mass. Which setup is right?
- 3 × 2 × 40 × 1,600 = 384,000 kg
- 3 × 2 × 1,600 = 9,600 kg
- 3 × 2 × 0.40 m³ × 1,600 kg per m³ = 3,840 kg
- 1,600 ÷ (3 × 2 × 0.40) ≈ 667 kg
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 B: 450 g ÷ 150 cm³ = 3.0 g/cm³, against A's 1.8
- Block A: its mass is greater, 540 g against 450 g
- Block A: its volume is greater, so it holds more matter
- Block A: 540 ÷ 300 = 1.8 beats 0.45 ÷ 150 = 0.003
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 sinks: volume 3.14 × 2² × 10 = 125.6 cm³, so 400 ÷ 125.6 ≈ 3.2 g/cm³
- It floats: volume 3.14 × 4² × 10 = 502.4 cm³, so 400 ÷ 502.4 ≈ 0.8 g/cm³
- It floats: 125.6 ÷ 400 ≈ 0.3 g/cm³
- It floats: 400 g is a light mass
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 is already larger than 0.24, so no conversion is needed
- Cork: balsa is 160 kg/m³ = 0.16 g/cm³, less than 0.24
- Balsa: 160 kg/m³ = 1.6 g/cm³, more than 0.24
- Balsa: 160 kg/m³ = 16 g/cm³, more than 0.24
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 1/100 of the real mass
- It has 1/10 of the real mass
- 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
A model tank has every length 1/20 of the real tank's. The real tank holds 8,000 liters. Ren finds the model's capacity. Which is right?
- 8,000 × 20 = 160,000 liters
- 8,000 ÷ 20³ = 1 liter
- 8,000 ÷ 20² = 20 liters
- 8,000 ÷ 20 = 400 liters
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 × 9
- Wood area × 27, soil volume × 27
- Wood area × 3, soil volume × 3
- Wood area × 9, soil volume × 27
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: 1 kg and 1.1 g/cm³
- Each half: 0.25 kg and 1.1 g/cm³
- Each half: 0.5 kg and still 1.1 g/cm³
- Each half: 0.5 kg and 0.55 g/cm³