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g Using a calculator, find the actual error in measuring volume if the radius was really 6.5 cm instead of 6 cm, and find the actual error if the radius was actually 5.5 cm instead of 6 cm. Compare these errors to the answer you got using differentials

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3 votes

Answer:

The answer is "
58.625 cm^3"

Explanation:

Consider the cube volume of x =6 cm.

Substitute x = 6 cm in the volume


V= x^3\\\\ V = (6)^3\\\\ V = 216

Therefore, whenever the cube volume


x=6 \ cm \ is \ V= 216 \ cm^3

Then consider the cube's volume

x = 6.5 cm.

Substitute x = 6.5 cm in the volume


V_1 = x^3\\V_1 = (6.5)^3\\V_1 = 274.625 \\ by using the calculator.

Therefore, when another cube volume


x = 6.5 cm \\\\ V_1 = 274.625 cm^3.

The real volume error x = 6.5 cm instead of x = 6 cm is calculated as,


dV= V_1-V\\


=274.625-216\\=58.625\\

Hence, the actual error in the volume when x = 6.5 cm instead of x = 6 cm is
58.625 \ cm^3.

User Ajmal Ansari
by
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