g The edge of a cube was measured to be 6 cm, with a maximum possible error of 0.5 cm. Use a differential to estimate the maximum possible error in computing the volume of the cube. (b) 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 thes

Complete question is;

(a) The edge of a cube was measured to be 6 cm, with a maximum possible error of 0.5 cm. Use a differential to estimate the maximum possible error in computing the volume of the cube.

(b) 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.

A) Maximum possible error = 54 cm³

B) i) The actual error of 58.625 cm³ is more than that gotten from the differential, so we will reject this radius of 6.5 cm.

(ii) The actual error of 49.625 cm³ gotten falls within range of the maximum error gotten from the differential so we can accept the radius of 5.5cm.

Step-by-step explanation:

The formula for volume of a cube is;

V(x) = x³

Where x is the length of the edge of the cube.

So, dV/dx = 3x²

When Δx is small like in this case, we can say that;

ΔV/Δx ≈ 3x²

So, ΔV ≈ 3x²•Δx

We are given;

Δx = 0.5 and x = 6.

Thus;

Maximum possible error = 3x²•Δx = 3 × 6² × 0.5 = 54 cm³

B) (i) If radius was 6.5,then;

Volume = 6.5³ = 274.625 cm³

Comparing to radius of 6cm;

Volume = 6³ = 216 cm³

So, actual error = 274.625 cm³ - 216 cm³ = 58.625 cm³

This actual error is more than that gotten from the maximum error from the Differential. So we will not accept this radius of 6.5cm.

ii) If radius was 5.5,then;

Volume = 5.5³ = 166.375 cm³

Comparing to radius of 6cm;

Volume = 6³ = 216 cm³

So, actual error = 216 cm³ - 166.375 cm³ = 49.625 cm³

This actual error gotten falls within range of the maximum error gotten from the differential so we can accept the radius of 5.5 cm.

not sure but it may be b, as i said i'm not sure.