If the length of a side of a cube is measured as 2.0 ± 0.1 m, what is the maximum possible error in the volume of the cube?
Practice Questions
1 question
Q1
If the length of a side of a cube is measured as 2.0 ± 0.1 m, what is the maximum possible error in the volume of the cube?
0.8 m³
0.4 m³
0.2 m³
0.1 m³
Volume V = L³. The maximum error in volume can be calculated using the formula: ΔV = 3L²ΔL. Here, ΔL = 0.1 m, L = 2.0 m, so ΔV = 3(2.0)²(0.1) = 1.2 m³.
Questions & Step-by-step Solutions
1 item
Q
Q: If the length of a side of a cube is measured as 2.0 ± 0.1 m, what is the maximum possible error in the volume of the cube?
Solution: Volume V = L³. The maximum error in volume can be calculated using the formula: ΔV = 3L²ΔL. Here, ΔL = 0.1 m, L = 2.0 m, so ΔV = 3(2.0)²(0.1) = 1.2 m³.
Steps: 8
Step 1: Understand that the volume of a cube is calculated using the formula V = L³, where L is the length of a side of the cube.
Step 2: Identify the given values: the length L = 2.0 m and the uncertainty in the length ΔL = 0.1 m.
Step 3: To find the maximum possible error in the volume, use the formula for maximum error in volume: ΔV = 3L²ΔL.
Step 4: Substitute the values into the formula: L = 2.0 m and ΔL = 0.1 m.
Step 5: Calculate L²: (2.0 m)² = 4.0 m².
Step 6: Multiply by 3: 3 * 4.0 m² = 12.0 m².
Step 7: Now multiply by ΔL: 12.0 m² * 0.1 m = 1.2 m³.
Step 8: Conclude that the maximum possible error in the volume of the cube is 1.2 m³.
