Let’s solve each problem step by step.
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Problem 1:
We are given:
- Pressure (P) = 39,200 Pa
- Density of freshwater (D) = 1000 kg/m³
- Gravity (g) = 9.8 m/s²
- We need to find depth H in
feet
- Conversion: 1 m = 3.28 ft
Formula:
P = D × g × H
Step 1: Rearrange formula to solve for H:
H = P / (D × g)
Step 2: Plug in numbers:
H = 39,200 / (1000 × 9.8)
H = 39,200 / 9800
H = 4 meters
Step 3: Convert meters to feet:
4 m × 3.28 ft/m = 13.12 ft
✔ Final Answer for Problem 1:
13.12 feet
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Problem 2:
We are given:
- Depth (H) = 3,840 m
- Density of seawater (D) = 1025 kg/m³
- Gravity (g) = 9.8 m/s²
- Find gauge pressure (P) in Pascals
Formula:
P = D × g × H
Step 1: Plug in numbers:
P = 1025 × 9.8 × 3840
Step 2: Multiply step by step:
First, 1025 × 9.8 = 10,045
Then, 10,045 × 3840 = ?
Let’s compute:
10,045 × 3840
= 10,045 × (3000 + 800 + 40)
= (10,045 × 3000) + (10,045 × 800) + (10,045 × 40)
Compute each:
- 10,045 × 3000 = 30,135,000
- 10,045 × 800 = 8,036,000
- 10,045 × 40 = 401,800
Add them:
30,135,000 + 8,036,000 = 38,171,000
38,171,000 + 401,800 =
38,572,800
✔ Final Answer for Problem 2:
38,572,800 Pa
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Problem 3:
We are given:
- Pressure (P) = 4.98 × 10⁵ Pa = 498,000 Pa
- Density (D) = 1000 kg/m³
- Gravity (g) = 9.8 m/s²
- Find depth H in
feet
- Conversion: 1 m = 3.28 ft
Formula:
P = D × g × H
Step 1: Rearrange:
H = P / (D × g)
Step 2: Plug in:
H = 498,000 / (1000 × 9.8)
H = 498,000 / 9800
H ≈ 50.8163 meters
Step 3: Convert to feet:
50.8163 × 3.28 ≈ ?
Calculate:
50 × 3.28 = 164
0.8163 × 3.28 ≈ 2.677
Total ≈ 164 + 2.677 =
166.677 ft
Rounded to two decimals:
166.68 ft
✔ Final Answer for Problem 3:
166.68 feet
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Final Answer:
Problem 1: 13.12 feet
Problem 2: 38,572,800 Pa
Problem 3: 166.68 feet
Parent Tip: Review the logic above to help your child master the concept of pressure problems worksheet.
