Fence worksheet

1. Posts: 16

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{130}{10}$$=13$$=\text{rounded up:}13$

2. Count posts: one more than the sections, because both ends need a post, plus your extra posts

   $13+1+2$$=16$

3. Count rails: 2 for each section

   $13\times 2$$=26$

4. Find how many pickets fill the fence: its length in inches ÷ the space each picket takes (its width plus the gap)

   $\frac{\mathrm{1,560}}{\left(4+2.3\right)}$$=247.619$

5. Add 6% extra for split or warped boards, then round up to whole pickets

   $247.619\times 1+0.06$$=262.4762$$=\text{rounded up:}263$

6. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times {6.5}^2-{3.4}^2\right)\times 28}{\mathrm{1,728}}$$=1.9634\text{\hspace{0.17em}ft³}$

7. Find bags per post: each 60 lb bag makes about 0.45 ft³ of concrete

   $\frac{1.9634}{0.45}$$=4.3632$

8. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{1.9634\times 16}{0.45}$$=69.8112$$=\text{rounded up:}70$

9. Add up the cost: how many you need times the price, for the posts, rails, pickets, bags

   $16\times \mathrm{\$13.00}+26\times \mathrm{\$4.00}+263\times \mathrm{\$4.00}+70\times \mathrm{\$7.00}$$=\mathrm{\$1,854.00}$

2. Posts: 13

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{116}{10}$$=11.6$$=\text{rounded up:}12$

2. Count posts: one more than the sections, because both ends need a post

   $12+1$$=13$

3. Count rails: 3 for each section

   $12\times 3$$=36$

4. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times 4^2-{3.2}^2\right)\times 26}{\mathrm{1,728}}$$=0.6022\text{\hspace{0.17em}ft³}$

5. Find bags per post: each 80 lb bag makes about 0.6 ft³ of concrete

   $\frac{0.6022}{0.6}$$=1.0037$

6. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{0.6022\times 13}{0.6}$$=13.0484$$=\text{rounded up:}14$

7. Add up the cost: how many you need times the price, for the posts, rails, bags

   $13\times \mathrm{\$14.00}+36\times \mathrm{\$6.00}+14\times \mathrm{\$6.00}$$=\mathrm{\$482.00}$

3. Posts: 14

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{90}{7}$$=12.8571$$=\text{rounded up:}13$

2. Count posts: one more than the sections, because both ends need a post

   $13+1$$=14$

3. Count rails: 2 for each section

   $13\times 2$$=26$

4. Find how many pickets fill the fence: its length in inches ÷ the picket width

   $\frac{\mathrm{1,080}}{5}$$=216$

5. Add 5% extra for split or warped boards, then round up to whole pickets

   $216\times 1+0.05$$=226.8$$=\text{rounded up:}227$

6. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times {4.5}^2-3^2\right)\times 36}{\mathrm{1,728}}$$=1.1379\text{\hspace{0.17em}ft³}$

7. Find bags per post: each 60 lb bag makes about 0.45 ft³ of concrete

   $\frac{1.1379}{0.45}$$=2.5286$

8. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{1.1379\times 14}{0.45}$$=35.4001$$=\text{rounded up:}36$

9. Add up the cost: how many you need times the price, for the posts, rails, pickets, bags

   $14\times \mathrm{\$14.00}+26\times \mathrm{\$6.00}+227\times \mathrm{\$2.00}+36\times \mathrm{\$7.00}$$=\mathrm{\$1,058.00}$

4. Posts: 16

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{105}{8}$$=13.125$$=\text{rounded up:}14$

2. Count posts: one more than the sections, because both ends need a post, plus your extra posts

   $14+1+1$$=16$

3. Count rails: 2 for each section

   $14\times 2$$=28$

4. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times 4^2-{4.2}^2\right)\times 33}{\mathrm{1,728}}$$=0.6231\text{\hspace{0.17em}ft³}$

5. Find bags per post: each 80 lb bag makes about 0.6 ft³ of concrete

   $\frac{0.6231}{0.6}$$=1.0384$

6. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{0.6231\times 16}{0.6}$$=16.6148$$=\text{rounded up:}17$

7. Add up the cost: how many you need times the price, for the posts, rails, bags

   $16\times \mathrm{\$13.00}+28\times \mathrm{\$5.00}+17\times \mathrm{\$6.00}$$=\mathrm{\$450.00}$

5. Posts: 11

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{98}{10}$$=9.8$$=\text{rounded up:}10$

2. Count posts: one more than the sections, because both ends need a post

   $10+1$$=11$

3. Count rails: 2 for each section

   $10\times 2$$=20$

4. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times {4.5}^2-3^2\right)\times 26}{\mathrm{1,728}}$$=0.8218\text{\hspace{0.17em}ft³}$

5. Find bags per post: each 60 lb bag makes about 0.45 ft³ of concrete

   $\frac{0.8218}{0.45}$$=1.8262$

6. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{0.8218\times 11}{0.45}$$=20.0881$$=\text{rounded up:}21$

7. Add up the cost: how many you need times the price, for the posts, rails, bags

   $11\times \mathrm{\$11.00}+20\times \mathrm{\$7.00}+21\times \mathrm{\$9.00}$$=\mathrm{\$450.00}$

6. Posts: 21

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{115}{6}$$=19.1667$$=\text{rounded up:}20$

2. Count posts: one more than the sections, because both ends need a post

   $20+1$$=21$

3. Count rails: 3 for each section

   $20\times 3$$=60$

4. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times {5.5}^2-{3.4}^2\right)\times 25}{\mathrm{1,728}}$$=1.2077\text{\hspace{0.17em}ft³}$

5. Find bags per post: each 40 lb bag makes about 0.3 ft³ of concrete

   $\frac{1.2077}{0.3}$$=4.0255$

6. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{1.2077\times 21}{0.3}$$=84.5359$$=\text{rounded up:}85$

7. Add up the cost: how many you need times the price, for the posts, rails, bags

   $21\times \mathrm{\$18.00}+60\times \mathrm{\$7.00}+85\times \mathrm{\$5.00}$$=\mathrm{\$1,223.00}$

7. Posts: 15

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{80}{6}$$=13.3333$$=\text{rounded up:}14$

2. Count posts: one more than the sections, because both ends need a post

   $14+1$$=15$

3. Count rails: 2 for each section

   $14\times 2$$=28$

4. Find how many pickets fill the fence: its length in inches ÷ the space each picket takes (its width plus the gap)

   $\frac{960}{\left(5.5+2.8\right)}$$=115.6627$

5. Add 5% extra for split or warped boards, then round up to whole pickets

   $115.6627\times 1+0.05$$=121.4458$$=\text{rounded up:}122$

6. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times {4.5}^2-4^2\right)\times 38}{\mathrm{1,728}}$$=1.0471\text{\hspace{0.17em}ft³}$

7. Find bags per post: each 60 lb bag makes about 0.45 ft³ of concrete

   $\frac{1.0471}{0.45}$$=2.327$

8. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{1.0471\times 15}{0.45}$$=34.9046$$=\text{rounded up:}35$

9. Add up the cost: how many you need times the price, for the posts, rails, pickets, bags

   $15\times \mathrm{\$15.00}+28\times \mathrm{\$5.00}+122\times \mathrm{\$3.00}+35\times \mathrm{\$5.00}$$=\mathrm{\$906.00}$

8. Posts: 16

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{100}{7}$$=14.2857$$=\text{rounded up:}15$

2. Count posts: one more than the sections, because both ends need a post

   $15+1$$=16$

3. Count rails: 2 for each section

   $15\times 2$$=30$

4. Find how many pickets fill the fence: its length in inches ÷ the picket width

   $\frac{\mathrm{1,200}}{5.5}$$=218.1818$

5. Add 6% extra for split or warped boards, then round up to whole pickets

   $218.1818\times 1+0.06$$=231.2727$$=\text{rounded up:}232$

6. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times 6^2-{2.6}^2\right)\times 26}{\mathrm{1,728}}$$=1.6\text{\hspace{0.17em}ft³}$

7. Find bags per post: each 60 lb bag makes about 0.45 ft³ of concrete

   $\frac{1.6}{0.45}$$=3.5555$

8. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{1.6\times 16}{0.45}$$=56.8883$$=\text{rounded up:}57$

9. Add up the cost: how many you need times the price, for the posts, rails, pickets, bags

   $16\times \mathrm{\$18.00}+30\times \mathrm{\$5.00}+232\times \mathrm{\$3.00}+57\times \mathrm{\$6.00}$$=\mathrm{\$1,476.00}$

9. Posts: 12

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{85}{8}$$=10.625$$=\text{rounded up:}11$

2. Count posts: one more than the sections, because both ends need a post

   $11+1$$=12$

3. Count rails: 2 for each section

   $11\times 2$$=22$

4. Find how many pickets fill the fence: its length in inches ÷ the picket width

   $\frac{\mathrm{1,020}}{6.5}$$=156.9231$

5. Add 4% extra for split or warped boards, then round up to whole pickets

   $156.9231\times 1+0.04$$=163.2$$=\text{rounded up:}164$

6. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times 7^2-{2.7}^2\right)\times 28}{\mathrm{1,728}}$$=2.3762\text{\hspace{0.17em}ft³}$

7. Find bags per post: each 60 lb bag makes about 0.45 ft³ of concrete

   $\frac{2.3762}{0.45}$$=5.2805$

8. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{2.3762\times 12}{0.45}$$=63.3664$$=\text{rounded up:}64$

9. Add up the cost: how many you need times the price, for the posts, rails, pickets, bags

   $12\times \mathrm{\$14.00}+22\times \mathrm{\$7.00}+164\times \mathrm{\$2.00}+64\times \mathrm{\$7.00}$$=\mathrm{\$1,098.00}$

10. Posts: 14

1. Divide the fence length by the post spacing to count sections. Round up, since a short last section still needs its own posts

   $\frac{110}{9}$$=12.2222$$=\text{rounded up:}13$

2. Count posts: one more than the sections, because both ends need a post

   $13+1$$=14$

3. Count rails: 3 for each section

   $13\times 3$$=39$

4. Find how many pickets fill the fence: its length in inches ÷ the picket width

   $\frac{\mathrm{1,320}}{5.5}$$=240$

5. Add 4% extra for split or warped boards, then round up to whole pickets

   $240\times 1+0.04$$=249.6$$=\text{rounded up:}250$

6. Find the concrete for one post: the round hole's space minus the space the post fills. Divide by 1,728 to turn cubic inches into cubic feet

   $\frac{\left(\pi \times {5.5}^2-{3.2}^2\right)\times 22}{\mathrm{1,728}}$$=1.0795\text{\hspace{0.17em}ft³}$

7. Find bags per post: each 80 lb bag makes about 0.6 ft³ of concrete

   $\frac{1.0795}{0.6}$$=1.7992$

8. Find the total bags for all posts. Round up only once, since a part bag carries over to the next hole

   $\frac{1.0795\times 14}{0.6}$$=25.1893$$=\text{rounded up:}26$

9. Add up the cost: how many you need times the price, for the posts, rails, pickets, bags

   $14\times \mathrm{\$14.00}+39\times \mathrm{\$7.00}+250\times \mathrm{\$2.00}+26\times \mathrm{\$5.00}$$=\mathrm{\$1,099.00}$