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Pipe Slope worksheet

Grades 6–7 · CCSS 7.RP.A.2.c, 6.RP.A.3.d

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

1.
Problem 1.
- Find: Slope from a fall
- Length of the run: 28 ft
- Drop from start to end: 6 in
- Compare with the minimum slope for: Drain pipe 2½ in or smaller
Find: Slope
Answer
2.
Problem 2.
- Find: Fall over a run
- Slope: 0.125 in per ft
- Length of the run: 15 ft
- Compare with the minimum slope for: Drain pipe 3 to 6 in
Find: Fall over the run
Answer
3.
Problem 3.
- Find: Fall over a run
- Slope: 0.5 in per ft
- Length of the run: 13 ft
- Compare with the minimum slope for: Drain pipe 3 to 6 in
Find: Fall over the run
Answer
4.
Problem 4.
- Find: Slope from a fall
- Length of the run: 18 ft
- Drop from start to end: 5 in
- Compare with the minimum slope for: No comparison
Find: Slope
Answer
5.
Problem 5.
- Find: Slope from a fall
- Length of the run: 18 ft
- Drop from start to end: 4 in
- Compare with the minimum slope for: No comparison
Find: Slope
Answer
6.
Problem 6.
- Find: Slope from a fall
- Length of the run: 16 ft
- Drop from start to end: 6 in
- Compare with the minimum slope for: Drain pipe 2½ in or smaller
Find: Slope
Answer
7.
Problem 7.
- Find: Fall over a run
- Slope: 0.5 in per ft
- Length of the run: 28 ft
- Compare with the minimum slope for: Drain pipe 8 in or larger
Find: Fall over the run
Answer
8.
Problem 8.
- Find: Slope from a fall
- Length of the run: 18 ft
- Drop from start to end: 6 in
- Compare with the minimum slope for: Drain pipe 2½ in or smaller
Find: Slope
Answer
9.
Problem 9.
- Find: Slope from a fall
- Length of the run: 22 ft
- Drop from start to end: 5 in
- Compare with the minimum slope for: Drain pipe 8 in or larger
Find: Slope
Answer
10.
Problem 10.
- Find: Fall over a run
- Slope: 0.25 in per ft
- Length of the run: 14 ft
- Compare with the minimum slope for: Drain pipe 8 in or larger
Find: Fall over the run
Answer

Answer key: Pipe Slope worksheet

1. Slope: 1.786%
1. Put the length in in, so it matches the fall
  $28 \times 12$ $= 336 in$
2. Divide the fall by the length and multiply by 100 to get the slope as a percent
  $\frac{6}{336} \times 100$ $= 1.785714%$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{1.785714}{100} \times 12$ $= 0.214286 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.017857$ $= 1.023 °$
2. Fall over the run: 1.875 in
1. Turn inches per foot into a percent: divide by the 12 inches in a foot, then multiply by 100
  $\frac{0.125}{12} \times 100$ $= 1.041667%$
2. Multiply the slope by the length to get the fall, in inches (1 ft = 12 in)
  $\frac{1.041667}{100} \times 15 \times 12$ $= 1.875 in$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{1.041667}{100} \times 12$ $= 0.125 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.010417$ $= 0.5968 °$
3. Fall over the run: 6.5 in
1. Turn inches per foot into a percent: divide by the 12 inches in a foot, then multiply by 100
  $\frac{0.5}{12} \times 100$ $= 4.166667%$
2. Multiply the slope by the length to get the fall, in inches (1 ft = 12 in)
  $\frac{4.166667}{100} \times 13 \times 12$ $= 6.5 in$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{4.166667}{100} \times 12$ $= 0.5 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.041667$ $= 2.3859 °$
4. Slope: 2.315%
1. Put the length in in, so it matches the fall
  $18 \times 12$ $= 216 in$
2. Divide the fall by the length and multiply by 100 to get the slope as a percent
  $\frac{5}{216} \times 100$ $= 2.314815%$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{2.314815}{100} \times 12$ $= 0.277778 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.023148$ $= 1.3261 °$
5. Slope: 1.852%
1. Put the length in in, so it matches the fall
  $18 \times 12$ $= 216 in$
2. Divide the fall by the length and multiply by 100 to get the slope as a percent
  $\frac{4}{216} \times 100$ $= 1.851852%$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{1.851852}{100} \times 12$ $= 0.222222 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.018519$ $= 1.0609 °$
6. Slope: 3.125%
1. Put the length in in, so it matches the fall
  $16 \times 12$ $= 192 in$
2. Divide the fall by the length and multiply by 100 to get the slope as a percent
  $\frac{6}{192} \times 100$ $= 3.125%$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{3.125}{100} \times 12$ $= 0.375 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.03125$ $= 1.7899 °$
7. Fall over the run: 14 in
1. Turn inches per foot into a percent: divide by the 12 inches in a foot, then multiply by 100
  $\frac{0.5}{12} \times 100$ $= 4.166667%$
2. Multiply the slope by the length to get the fall, in inches (1 ft = 12 in)
  $\frac{4.166667}{100} \times 28 \times 12$ $= 14 in$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{4.166667}{100} \times 12$ $= 0.5 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.041667$ $= 2.3859 °$
8. Slope: 2.778%
1. Put the length in in, so it matches the fall
  $18 \times 12$ $= 216 in$
2. Divide the fall by the length and multiply by 100 to get the slope as a percent
  $\frac{6}{216} \times 100$ $= 2.777778%$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{2.777778}{100} \times 12$ $= 0.333333 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.027778$ $= 1.5911 °$
9. Slope: 1.894%
1. Put the length in in, so it matches the fall
  $22 \times 12$ $= 264 in$
2. Divide the fall by the length and multiply by 100 to get the slope as a percent
  $\frac{5}{264} \times 100$ $= 1.893939%$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{1.893939}{100} \times 12$ $= 0.227273 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.018939$ $= 1.085 °$
10. Fall over the run: 3.5 in
1. Turn inches per foot into a percent: divide by the 12 inches in a foot, then multiply by 100
  $\frac{0.25}{12} \times 100$ $= 2.083333%$
2. Multiply the slope by the length to get the fall, in inches (1 ft = 12 in)
  $\frac{2.083333}{100} \times 14 \times 12$ $= 3.5 in$
3. Turn the percent into inches per foot: divide by 100, then multiply by 12
  $\frac{2.083333}{100} \times 12$ $= 0.25 in/ft$
4. Find the angle below level from the slope, using arctan (which turns a slope into an angle)
  $θ$ $= arctan 0.020833$ $= 1.1935 °$