Model a real object with a shape, and design problems with limits
Grade 10 Math Worksheet
Circle the best answer.
Ari's grain silo is a cylinder (radius 3 m, wall height 8 m) topped by a hemisphere. Using π = 3.14, what is its volume?
- 282.6 m³
- 226.1 m³
- 339.1 m³
- 254.3 m³
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?
- 150.7 cm³
- 94.2 cm³
- 339.1 cm³
- 207.2 cm³
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
- 500 m²
- 10 m²
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?
- 196 cm³
- 867 cm³
- 588 cm³
- 1,200 cm³
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 B, by about 6.3 cm²
- Can A, by 2 cm²
- Neither: the same volume means the same metal.
- Can A, by about 6.3 cm²
A 1:20 scale model of Milo's water tank holds 5 L. How many liters does the real tank hold?
- 100 L
- 40,000 L
- 2,000 L
- 8,000 L
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
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?
- 10,000 minutes
- 10 minutes
- 13.3 minutes
- 120 minutes
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
- 12
- 9
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?
- 44.8 m²
- 57.7 m²
- 24 m²
- About 28.8 m²