Concrete worksheet

1. Concrete to order: 1.17 m³

1. Multiply length × width × thickness to get the space the concrete fills. The thickness is converted to m first so all the units match

   $4\times 3\times \frac{9}{100}$$=1.08\text{\hspace{0.17em}m³}$

2. Add 8% extra, because some concrete is always lost to uneven ground and spills

   $1.08\times 1+0.08$$=1.1664\text{\hspace{0.17em}m³}$

3. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{\mathrm{1,166.4}\text{\hspace{0.17em}L}}{8.5\text{\hspace{0.17em}L}}$$=137.2235$$=\text{rounded up:}138$

4. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{\mathrm{1,166.4}\text{\hspace{0.17em}L}}{12.7\text{\hspace{0.17em}L}}$$=91.8425$$=\text{rounded up:}92$

5. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{\mathrm{1,166.4}\text{\hspace{0.17em}L}}{17\text{\hspace{0.17em}L}}$$=68.6118$$=\text{rounded up:}69$

6. Ready-mix cost: the amount to order × the price per m³ (delivery fees not included)

   $1.1664\text{\hspace{0.17em}m³}\times \mathrm{\$210.00}$$=\mathrm{\$244.94}$

7. Bag cost: the number of 80 lb bags × the price per bag

   $69\times \mathrm{\$5.50}$$=\mathrm{\$379.50}$

2. Concrete to order: 0.13 m³

1. Find the area of the hole's round opening: π × (half the diameter)², with the diameter converted to m

   $\pi \times {\left(\frac{\frac{22}{100}}{2}\right)}^2$$=0.038013\text{\hspace{0.17em}m²}$

2. Find the area the square post takes up: width × width

   ${\left(\frac{7}{100}\right)}^2$$=0.0049\text{\hspace{0.17em}m²}$

3. Concrete only fills the gap around the post, so take the post's area away from the hole's, then multiply by the depth

   $\left(0.038013-0.0049\right)\times \frac{70}{100}$$=0.023179\text{\hspace{0.17em}m³}$

4. Multiply by the number of holes for the total

   $0.023179\times 5$$=0.115896\text{\hspace{0.17em}m³}$

5. Add 11% extra, because some concrete is always lost to uneven ground and spills

   $0.115896\times 1+0.11$$=0.128645\text{\hspace{0.17em}m³}$

6. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{128.645058\text{\hspace{0.17em}L}}{8.5\text{\hspace{0.17em}L}}$$=15.1347$$=\text{rounded up:}16$

7. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{128.645058\text{\hspace{0.17em}L}}{12.7\text{\hspace{0.17em}L}}$$=10.1295$$=\text{rounded up:}11$

8. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{128.645058\text{\hspace{0.17em}L}}{17\text{\hspace{0.17em}L}}$$=7.5674$$=\text{rounded up:}8$

9. Ready-mix cost: the amount to order × the price per m³ (delivery fees not included)

   $0.128645\text{\hspace{0.17em}m³}\times \mathrm{\$200.00}$$=\mathrm{\$25.73}$

10. Bag cost: the number of 80 lb bags × the price per bag

    $8\times \mathrm{\$9.00}$$=\mathrm{\$72.00}$

3. Concrete to order: 0.35 yd³

1. Find the area of the hole's round opening: π × (half the diameter)², with the diameter converted to ft

   $\pi \times {\left(\frac{\frac{11}{12}}{2}\right)}^2$$=0.659953\text{\hspace{0.17em}ft²}$

2. Find the area the square post takes up: width × width

   ${\left(\frac{3.4}{12}\right)}^2$$=0.080278\text{\hspace{0.17em}ft²}$

3. Concrete only fills the gap around the post, so take the post's area away from the hole's, then multiply by the depth

   $\left(0.659953-0.080278\right)\times \frac{36}{12}$$=1.739025\text{\hspace{0.17em}ft³}$

4. Multiply by the number of holes for the total

   $1.739025\times 5$$=8.695123\text{\hspace{0.17em}ft³}$

5. Divide by 27 to get cubic yards, the unit ready-mix is sold in (1 yd³ = 27 ft³)

   $\frac{8.695123}{27}$$=0.322042\text{\hspace{0.17em}yd³}$

6. Add 10% extra, because some concrete is always lost to uneven ground and spills

   $0.322042\times 1+0.1$$=0.354246\text{\hspace{0.17em}yd³}$

7. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{9.564635\text{\hspace{0.17em}ft³}}{0.3\text{\hspace{0.17em}ft³}}$$=31.8821$$=\text{rounded up:}32$

8. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{9.564635\text{\hspace{0.17em}ft³}}{0.45\text{\hspace{0.17em}ft³}}$$=21.2547$$=\text{rounded up:}22$

9. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{9.564635\text{\hspace{0.17em}ft³}}{0.6\text{\hspace{0.17em}ft³}}$$=15.9411$$=\text{rounded up:}16$

10. Ready-mix cost: the amount to order × the price per yd³ (delivery fees not included)

    $0.354246\text{\hspace{0.17em}yd³}\times \mathrm{\$120.00}$$=\mathrm{\$42.51}$

11. Bag cost: the number of 80 lb bags × the price per bag

    $16\times \mathrm{\$5.50}$$=\mathrm{\$88.00}$

4. Concrete to order: 0.38 yd³

1. Find the area of the column's round face: π × (half the diameter)². The diameter is converted to ft first so all the units match

   $\pi \times {\left(\frac{\frac{12}{12}}{2}\right)}^2$$=0.785398\text{\hspace{0.17em}ft²}$

2. Multiply that area by the height to get the space inside one piece, then by the number of pieces

   $0.785398\times 4\times 3$$=9.424778\text{\hspace{0.17em}ft³}$

3. Divide by 27 to get cubic yards, the unit ready-mix is sold in (1 yd³ = 27 ft³)

   $\frac{9.424778}{27}$$=0.349066\text{\hspace{0.17em}yd³}$

4. Add 9% extra, because some concrete is always lost to uneven ground and spills

   $0.349066\times 1+0.09$$=0.380482\text{\hspace{0.17em}yd³}$

5. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{10.273008\text{\hspace{0.17em}ft³}}{0.3\text{\hspace{0.17em}ft³}}$$=34.2434$$=\text{rounded up:}35$

6. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{10.273008\text{\hspace{0.17em}ft³}}{0.45\text{\hspace{0.17em}ft³}}$$=22.8289$$=\text{rounded up:}23$

7. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{10.273008\text{\hspace{0.17em}ft³}}{0.6\text{\hspace{0.17em}ft³}}$$=17.1217$$=\text{rounded up:}18$

8. Ready-mix cost: the amount to order × the price per yd³ (delivery fees not included)

   $0.380482\text{\hspace{0.17em}yd³}\times \mathrm{\$180.00}$$=\mathrm{\$68.49}$

9. Bag cost: the number of 80 lb bags × the price per bag

   $18\times \mathrm{\$9.00}$$=\mathrm{\$162.00}$

5. Concrete to order: 0.15 m³

1. Find the area of the column's round face: π × (half the diameter)². The diameter is converted to m first so all the units match

   $\pi \times {\left(\frac{\frac{38}{100}}{2}\right)}^2$$=0.113411\text{\hspace{0.17em}m²}$

2. Multiply that area by the height to get the space inside one piece, then by the number of pieces

   $0.113411\times 1.2\times 1$$=0.136094\text{\hspace{0.17em}m³}$

3. Add 10% extra, because some concrete is always lost to uneven ground and spills

   $0.136094\times 1+0.1$$=0.149703\text{\hspace{0.17em}m³}$

4. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{149.703173\text{\hspace{0.17em}L}}{8.5\text{\hspace{0.17em}L}}$$=17.6121$$=\text{rounded up:}18$

5. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{149.703173\text{\hspace{0.17em}L}}{12.7\text{\hspace{0.17em}L}}$$=11.7877$$=\text{rounded up:}12$

6. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{149.703173\text{\hspace{0.17em}L}}{17\text{\hspace{0.17em}L}}$$=8.8061$$=\text{rounded up:}9$

7. Ready-mix cost: the amount to order × the price per m³ (delivery fees not included)

   $0.149703\text{\hspace{0.17em}m³}\times \mathrm{\$190.00}$$=\mathrm{\$28.44}$

8. Bag cost: the number of 80 lb bags × the price per bag

   $9\times \mathrm{\$6.00}$$=\mathrm{\$54.00}$

6. Concrete to order: 1.61 yd³

1. Multiply length × width × thickness to get the space the concrete fills. The thickness is converted to ft first so all the units match

   $12\times 10\times \frac{4}{12}$$=40\text{\hspace{0.17em}ft³}$

2. Divide by 27 to get cubic yards, the unit ready-mix is sold in (1 yd³ = 27 ft³)

   $\frac{40}{27}$$=1.481481\text{\hspace{0.17em}yd³}$

3. Add 9% extra, because some concrete is always lost to uneven ground and spills

   $1.481481\times 1+0.09$$=1.614815\text{\hspace{0.17em}yd³}$

4. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{43.6\text{\hspace{0.17em}ft³}}{0.3\text{\hspace{0.17em}ft³}}$$=145.3333$$=\text{rounded up:}146$

5. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{43.6\text{\hspace{0.17em}ft³}}{0.45\text{\hspace{0.17em}ft³}}$$=96.8889$$=\text{rounded up:}97$

6. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{43.6\text{\hspace{0.17em}ft³}}{0.6\text{\hspace{0.17em}ft³}}$$=72.6667$$=\text{rounded up:}73$

7. Ready-mix cost: the amount to order × the price per yd³ (delivery fees not included)

   $1.614815\text{\hspace{0.17em}yd³}\times \mathrm{\$200.00}$$=\mathrm{\$322.96}$

8. Bag cost: the number of 80 lb bags × the price per bag

   $73\times \mathrm{\$5.40}$$=\mathrm{\$394.20}$

7. Concrete to order: 0.12 yd³

1. Find the area of the tube's ring-shaped face: the outer circle minus the empty core, worked out in ft

   $\frac{\pi }{4}\times \left({1.75}^2-{1.333333}^2\right)$$=1.009018\text{\hspace{0.17em}ft²}$

2. Multiply that area by the height to get the space inside one piece, then by the number of pieces

   $1.009018\times 3\times 1$$=3.027055\text{\hspace{0.17em}ft³}$

3. Divide by 27 to get cubic yards, the unit ready-mix is sold in (1 yd³ = 27 ft³)

   $\frac{3.027055}{27}$$=0.112113\text{\hspace{0.17em}yd³}$

4. Add 10% extra, because some concrete is always lost to uneven ground and spills

   $0.112113\times 1+0.1$$=0.123324\text{\hspace{0.17em}yd³}$

5. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{3.329761\text{\hspace{0.17em}ft³}}{0.3\text{\hspace{0.17em}ft³}}$$=11.0992$$=\text{rounded up:}12$

6. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{3.329761\text{\hspace{0.17em}ft³}}{0.45\text{\hspace{0.17em}ft³}}$$=7.3995$$=\text{rounded up:}8$

7. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{3.329761\text{\hspace{0.17em}ft³}}{0.6\text{\hspace{0.17em}ft³}}$$=5.5496$$=\text{rounded up:}6$

8. Ready-mix cost: the amount to order × the price per yd³ (delivery fees not included)

   $0.123324\text{\hspace{0.17em}yd³}\times \mathrm{\$140.00}$$=\mathrm{\$17.27}$

9. Bag cost: the number of 80 lb bags × the price per bag

   $6\times \mathrm{\$5.80}$$=\mathrm{\$34.80}$

8. Concrete to order: 1.19 m³

1. Multiply length × width × thickness to get the space the concrete fills. The thickness is converted to m first so all the units match

   $3\times 3\times \frac{12}{100}$$=1.08\text{\hspace{0.17em}m³}$

2. Add 10% extra, because some concrete is always lost to uneven ground and spills

   $1.08\times 1+0.1$$=1.188\text{\hspace{0.17em}m³}$

3. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{\mathrm{1,188}\text{\hspace{0.17em}L}}{8.5\text{\hspace{0.17em}L}}$$=139.7647$$=\text{rounded up:}140$

4. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{\mathrm{1,188}\text{\hspace{0.17em}L}}{12.7\text{\hspace{0.17em}L}}$$=93.5433$$=\text{rounded up:}94$

5. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{\mathrm{1,188}\text{\hspace{0.17em}L}}{17\text{\hspace{0.17em}L}}$$=69.8824$$=\text{rounded up:}70$

6. Ready-mix cost: the amount to order × the price per m³ (delivery fees not included)

   $1.188\text{\hspace{0.17em}m³}\times \mathrm{\$235.00}$$=\mathrm{\$279.18}$

7. Bag cost: the number of 80 lb bags × the price per bag

   $70\times \mathrm{\$6.20}$$=\mathrm{\$434.00}$

9. Concrete to order: 0.2 yd³

1. Find the area of the column's round face: π × (half the diameter)². The diameter is converted to ft first so all the units match

   $\pi \times {\left(\frac{\frac{15}{12}}{2}\right)}^2$$=1.227185\text{\hspace{0.17em}ft²}$

2. Multiply that area by the height to get the space inside one piece, then by the number of pieces

   $1.227185\times 4\times 1$$=4.908739\text{\hspace{0.17em}ft³}$

3. Divide by 27 to get cubic yards, the unit ready-mix is sold in (1 yd³ = 27 ft³)

   $\frac{4.908739}{27}$$=0.181805\text{\hspace{0.17em}yd³}$

4. Add 10% extra, because some concrete is always lost to uneven ground and spills

   $0.181805\times 1+0.1$$=0.199986\text{\hspace{0.17em}yd³}$

5. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{5.399612\text{\hspace{0.17em}ft³}}{0.3\text{\hspace{0.17em}ft³}}$$=17.9987$$=\text{rounded up:}18$

6. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{5.399612\text{\hspace{0.17em}ft³}}{0.45\text{\hspace{0.17em}ft³}}$$=11.9991$$=\text{rounded up:}12$

7. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{5.399612\text{\hspace{0.17em}ft³}}{0.6\text{\hspace{0.17em}ft³}}$$=8.9994$$=\text{rounded up:}9$

8. Ready-mix cost: the amount to order × the price per yd³ (delivery fees not included)

   $0.199986\text{\hspace{0.17em}yd³}\times \mathrm{\$200.00}$$=\mathrm{\$40.00}$

9. Bag cost: the number of 80 lb bags × the price per bag

   $9\times \mathrm{\$5.50}$$=\mathrm{\$49.50}$

10. Concrete to order: 0.08 m³

1. Find the area of the column's round face: π × (half the diameter)². The diameter is converted to m first so all the units match

   $\pi \times {\left(\frac{\frac{30}{100}}{2}\right)}^2$$=0.070686\text{\hspace{0.17em}m²}$

2. Multiply that area by the height to get the space inside one piece, then by the number of pieces

   $0.070686\times 1\times 1$$=0.070686\text{\hspace{0.17em}m³}$

3. Add 7% extra, because some concrete is always lost to uneven ground and spills

   $0.070686\times 1+0.07$$=0.075634\text{\hspace{0.17em}m³}$

4. 40 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{75.633843\text{\hspace{0.17em}L}}{8.5\text{\hspace{0.17em}L}}$$=8.8981$$=\text{rounded up:}9$

5. 60 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{75.633843\text{\hspace{0.17em}L}}{12.7\text{\hspace{0.17em}L}}$$=5.9554$$=\text{rounded up:}6$

6. 80 lb bags: divide the concrete needed by how much one bag makes, then round up, since you can't buy part of a bag

   $\frac{75.633843\text{\hspace{0.17em}L}}{17\text{\hspace{0.17em}L}}$$=4.449$$=\text{rounded up:}5$

7. Ready-mix cost: the amount to order × the price per m³ (delivery fees not included)

   $0.075634\text{\hspace{0.17em}m³}\times \mathrm{\$210.00}$$=\mathrm{\$15.88}$

8. Bag cost: the number of 80 lb bags × the price per bag

   $5\times \mathrm{\$8.00}$$=\mathrm{\$40.00}$