Question

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?

Answer 1

Answer:

Step-by-step explanation:

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.