the radius of a spherical diamond is measured as 6 cm with an error of 0. 04 cm .Obtain the approximate error in calculating its volume. If the cost of 1 cm cube diamond isRs. 1600 .what is the loss of the buyer of the Diamond .what lesson do you learn?
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Given
the radius of a spherical diamond is measured as 6 cm with an error of 0. 04 cm .Obtain the approximate error in calculating its volume. If the cost...
Given radius of the sphere r = 6 cm, error in measurement of radius Δr = 0.04 cm
We know that
Volume of sphere = 4/3 π r^3
Δ v = dv / dr x Δr
= d(4/3 π r^3) / dr x Δr
= 4/3 π 3r^2 x 0.04
= 4π r^2 x 0.04
= 4 π (6)^2 x 0.04
= 5.76 π cm^3
= 18.086 cm^3
So cost of 1 cm^3 is Rs 1600
Therefore cost of 18.086 cm^3 will be 1600 x 18.086 = Rs 28,938
So the loss of diamond will be 18.086 cm^3. So we need to check the error while measuring.
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