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Approximate the relative error in surface area when the edges of a 2x2x2 m² cube are mismeasured by 2 cm. O 0.25 O 0.0025 O 0.01 01

Answer :

The given data is a cube with an edge length of 2m and a surface area of 24m².

Want to find out the relative error in surface area when the edges of a cube are mismeasured by 2 cm?

The formula for the surface area of a cube: Surface [tex]Area = 6a²[/tex]where a is the edge lengthThe formula for the relative error isRelative [tex]Error = (Error / Exact value) * 100%Let's[/tex]solve the questionSolution: Given cube edge [tex]length (a) = 2 mExact value of Surface Area of cube = 6a² = 6 × 2² = 24 m²[/tex]Mismeasured edge length [tex](a') = 2 m + 2 cm = 2.02 mLength error (Δa) = |a - a'| = |2 - 2.02| = 0.02[/tex]mExact value of Surface[tex]Area of cube = 6a² = 6 × 2² = 24 m²Approximated Surface Area (A') = 6a'² = 6 × (2.02)² = 24.48 m²[/tex][tex]Surface Area Error (ΔA) = |A' - A| = |24.48 - 24| = 0.48 m²Relative Error = (Error / Exact value) * 100%Relative Error = (0.48/24) * 100%Relative Error = 0.02 * 100%Relative Error = 2%The relative error in surface area is 2%.[/tex]

Therefore, the correct option is 0.02.

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