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Gravel worksheet

Grades 6–7 · CCSS 6.G.A.2, 6.RP.A.3.d, 7.G.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Units: Metric (meters, cm, t/m³)
- Area shape: Rectangle
- Length: 8 m
- Width: 3 m
- Depth: 7 cm
- Gravel density: 1.2 t/m³
- Extra for compaction and waste: 10%
- Bulk price (optional): $45 per tonne
- Bag weight, if buying bags: 22 kg
- Price per bag (optional): $6
Find: Gravel to order
Answer
2.
Problem 2.
- Units: Metric (meters, cm, t/m³)
- Area shape: Circle
- Diameter: 3 m
- Depth: 6 cm
- Gravel density: 1.2 t/m³
- Extra for compaction and waste: 11%
- Bulk price (optional): $50 per tonne
- Bag weight, if buying bags: 36 kg
- Price per bag (optional): $6.30
Find: Gravel to order
Answer
3.
Problem 3.
- Units: Metric (meters, cm, t/m³)
- Area shape: Rectangle
- Length: 8 m
- Width: 3 m
- Depth: 8 cm
- Gravel density: 1.4 t/m³
- Extra for compaction and waste: 10%
- Bulk price (optional): $38 per tonne
- Bag weight, if buying bags: 22 kg
- Price per bag (optional): $3.80
Find: Gravel to order
Answer
4.
Problem 4.
- Units: US (feet, inches, lb/yd³)
- Area shape: Circle
- Diameter: 9 ft
- Depth: 3 in
- Gravel density: 3,200 lb/yd³
- Extra for compaction and waste: 9%
- Bulk price (optional): $40 per US ton
- Bag weight, if buying bags: 56 lb
- Price per bag (optional): $4.80
Find: Gravel to order
Answer
5.
Problem 5.
- Units: Metric (meters, cm, t/m³)
- Area shape: Rectangle
- Length: 8 m
- Width: 2 m
- Depth: 10 cm
- Gravel density: 1 t/m³
- Extra for compaction and waste: 8%
- Bulk price (optional): $54 per tonne
- Bag weight, if buying bags: 24 kg
- Price per bag (optional): $5.80
Find: Gravel to order
Answer
6.
Problem 6.
- Units: Metric (meters, cm, t/m³)
- Area shape: Circle
- Diameter: 2 m
- Depth: 8 cm
- Gravel density: 1.5 t/m³
- Extra for compaction and waste: 8%
- Bulk price (optional): $45 per tonne
- Bag weight, if buying bags: 28 kg
- Price per bag (optional): $4.50
Find: Gravel to order
Answer
7.
Problem 7.
- Units: Metric (meters, cm, t/m³)
- Area shape: Rectangle
- Length: 5 m
- Width: 3 m
- Depth: 8 cm
- Gravel density: 1.3 t/m³
- Extra for compaction and waste: 9%
- Bulk price (optional): $40 per tonne
- Bag weight, if buying bags: 18 kg
- Price per bag (optional): $6
Find: Gravel to order
Answer
8.
Problem 8.
- Units: Metric (meters, cm, t/m³)
- Area shape: Circle
- Diameter: 3 m
- Depth: 8 cm
- Gravel density: 1 t/m³
- Extra for compaction and waste: 8%
- Bulk price (optional): $60 per tonne
- Bag weight, if buying bags: 22 kg
- Price per bag (optional): $6
Find: Gravel to order
Answer
9.
Problem 9.
- Units: Metric (meters, cm, t/m³)
- Area shape: Rectangle
- Length: 7 m
- Width: 4 m
- Depth: 6 cm
- Gravel density: 1.4 t/m³
- Extra for compaction and waste: 9%
- Bulk price (optional): $38 per tonne
- Bag weight, if buying bags: 22 kg
- Price per bag (optional): $6.20
Find: Gravel to order
Answer
10.
Problem 10.
- Units: Metric (meters, cm, t/m³)
- Area shape: Circle
- Diameter: 3 m
- Depth: 10 cm
- Gravel density: 1.6 t/m³
- Extra for compaction and waste: 13%
- Bulk price (optional): $45 per tonne
- Bag weight, if buying bags: 25 kg
- Price per bag (optional): $6.20
Find: Gravel to order
Answer

Answer key: Gravel worksheet

1. Gravel to order: 1.85 m³
1. Find the area by multiplying the length by the width
  $8 \times 3$ $= 24 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $24 \times \frac{7}{100}$ $= 1.68 m³$
3. Add 10% extra, because gravel packs down and some is lost while spreading
  $1.68 \times 1 + 0.1$ $= 1.848 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $1.848 \times 1.2$ $= 2.2176 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $2.2176 t \times $45.00$ $= $99.79$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{2,217.6 kg}{22 kg}$ $= 100.8$ $= rounded up: 101$
7. Find the cost in bags: the number of bags times the price of one bag
  $101 \times $6.00$ $= $606.00$
2. Gravel to order: 0.47 m³
1. Find the area of the circle: π (about 3.14) times half the diameter, squared
  $π \times {(\frac{3}{2})}^{2}$ $= 7.068583 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $7.068583 \times \frac{6}{100}$ $= 0.424115 m³$
3. Add 11% extra, because gravel packs down and some is lost while spreading
  $0.424115 \times 1 + 0.11$ $= 0.470768 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $0.470768 \times 1.2$ $= 0.564921 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $0.564921 t \times $50.00$ $= $28.25$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{564.921191 kg}{36 kg}$ $= 15.6923$ $= rounded up: 16$
7. Find the cost in bags: the number of bags times the price of one bag
  $16 \times $6.30$ $= $100.80$
3. Gravel to order: 2.11 m³
1. Find the area by multiplying the length by the width
  $8 \times 3$ $= 24 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $24 \times \frac{8}{100}$ $= 1.92 m³$
3. Add 10% extra, because gravel packs down and some is lost while spreading
  $1.92 \times 1 + 0.1$ $= 2.112 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $2.112 \times 1.4$ $= 2.9568 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $2.9568 t \times $38.00$ $= $112.36$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{2,956.8 kg}{22 kg}$ $= 134.4$ $= rounded up: 135$
7. Find the cost in bags: the number of bags times the price of one bag
  $135 \times $3.80$ $= $513.00$
4. Gravel to order: 0.64 yd³
1. Find the area of the circle: π (about 3.14) times half the diameter, squared
  $π \times {(\frac{9}{2})}^{2}$ $= 63.617251 ft²$
2. Find the volume: the area times the depth, after turning inches into feet (÷ 12) so the units match
  $63.617251 \times \frac{3}{12}$ $= 15.904313 ft³$
3. Turn cubic feet into cubic yards, since 27 cubic feet make 1 cubic yard
  $\frac{15.904313}{27}$ $= 0.589049 yd³$
4. Add 9% extra, because gravel packs down and some is lost while spreading
  $0.589049 \times 1 + 0.09$ $= 0.642063 yd³$
5. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $0.642063 \times 3,200$ $= 2,054.601595 lb$
6. Turn pounds into US tons, since a US ton is 2,000 lb
  $\frac{2,054.601595}{2,000}$ $= 1.027301 tons$
7. Find the bulk cost: the amount to order times the price (delivery not included)
  $1.027301 tons \times $40.00$ $= $41.09$
8. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{2,054.601595 lb}{56 lb}$ $= 36.6893$ $= rounded up: 37$
9. Find the cost in bags: the number of bags times the price of one bag
  $37 \times $4.80$ $= $177.60$
5. Gravel to order: 1.73 m³
1. Find the area by multiplying the length by the width
  $8 \times 2$ $= 16 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $16 \times \frac{10}{100}$ $= 1.6 m³$
3. Add 8% extra, because gravel packs down and some is lost while spreading
  $1.6 \times 1 + 0.08$ $= 1.728 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $1.728 \times 1$ $= 1.728 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $1.728 t \times $54.00$ $= $93.31$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{1,728 kg}{24 kg}$ $= 72$ $= rounded up: 72$
7. Find the cost in bags: the number of bags times the price of one bag
  $72 \times $5.80$ $= $417.60$
6. Gravel to order: 0.27 m³
1. Find the area of the circle: π (about 3.14) times half the diameter, squared
  $π \times {(\frac{2}{2})}^{2}$ $= 3.141593 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $3.141593 \times \frac{8}{100}$ $= 0.251327 m³$
3. Add 8% extra, because gravel packs down and some is lost while spreading
  $0.251327 \times 1 + 0.08$ $= 0.271434 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $0.271434 \times 1.5$ $= 0.40715 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $0.40715 t \times $45.00$ $= $18.32$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{407.150408 kg}{28 kg}$ $= 14.5411$ $= rounded up: 15$
7. Find the cost in bags: the number of bags times the price of one bag
  $15 \times $4.50$ $= $67.50$
7. Gravel to order: 1.31 m³
1. Find the area by multiplying the length by the width
  $5 \times 3$ $= 15 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $15 \times \frac{8}{100}$ $= 1.2 m³$
3. Add 9% extra, because gravel packs down and some is lost while spreading
  $1.2 \times 1 + 0.09$ $= 1.308 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $1.308 \times 1.3$ $= 1.7004 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $1.7004 t \times $40.00$ $= $68.02$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{1,700.4 kg}{18 kg}$ $= 94.4667$ $= rounded up: 95$
7. Find the cost in bags: the number of bags times the price of one bag
  $95 \times $6.00$ $= $570.00$
8. Gravel to order: 0.61 m³
1. Find the area of the circle: π (about 3.14) times half the diameter, squared
  $π \times {(\frac{3}{2})}^{2}$ $= 7.068583 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $7.068583 \times \frac{8}{100}$ $= 0.565487 m³$
3. Add 8% extra, because gravel packs down and some is lost while spreading
  $0.565487 \times 1 + 0.08$ $= 0.610726 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $0.610726 \times 1$ $= 0.610726 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $0.610726 t \times $60.00$ $= $36.64$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{610.725612 kg}{22 kg}$ $= 27.7603$ $= rounded up: 28$
7. Find the cost in bags: the number of bags times the price of one bag
  $28 \times $6.00$ $= $168.00$
9. Gravel to order: 1.83 m³
1. Find the area by multiplying the length by the width
  $7 \times 4$ $= 28 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $28 \times \frac{6}{100}$ $= 1.68 m³$
3. Add 9% extra, because gravel packs down and some is lost while spreading
  $1.68 \times 1 + 0.09$ $= 1.8312 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $1.8312 \times 1.4$ $= 2.56368 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $2.56368 t \times $38.00$ $= $97.42$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{2,563.68 kg}{22 kg}$ $= 116.5309$ $= rounded up: 117$
7. Find the cost in bags: the number of bags times the price of one bag
  $117 \times $6.20$ $= $725.40$
10. Gravel to order: 0.8 m³
1. Find the area of the circle: π (about 3.14) times half the diameter, squared
  $π \times {(\frac{3}{2})}^{2}$ $= 7.068583 m²$
2. Find the volume: the area times the depth, after turning centimeters into meters (÷ 100) so the units match
  $7.068583 \times \frac{10}{100}$ $= 0.706858 m³$
3. Add 13% extra, because gravel packs down and some is lost while spreading
  $0.706858 \times 1 + 0.13$ $= 0.79875 m³$
4. Find the weight: the volume times the density (how much one unit of this stone weighs)
  $0.79875 \times 1.6$ $= 1.278 t$
5. Find the bulk cost: the amount to order times the price (delivery not included)
  $1.278 t \times $45.00$ $= $57.51$
6. Find the bags: the weight to order divided by one bag's weight, rounded up to whole bags
  $\frac{1,277.999891 kg}{25 kg}$ $= 51.12$ $= rounded up: 52$
7. Find the cost in bags: the number of bags times the price of one bag
  $52 \times $6.20$ $= $322.40$