The edge of a cube was measured to be 8 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. (this next part is ungraded, just for fun. using a calculator, find the actual error in measuring volume if the radius was really 8.5 cm instead of 8 cm, and find the actual error if the radius was actually 7.5 cm instead of 8 cm. compare these errors to the answer you got using differentials).

96 cc

102.125 cc

90.125 cc

Step-by-step explanation:

Let V(x) the volume of a cube of edge x cm. Then

The maximum possible error in computing the volume of the cube would be

V(8+0.5) - V(8)

By approximating with the derivative, we know

V(8+0.5) ≅ V(8) +0.5V'(8)

hence

V(8+0.5) - V(8) ≅ 0.5V'(8)  

But

and maximum possible error in computing the volume of the cube would be approximately 0.5*192 = 96 cc.

find the actual error in measuring volume if the radius was really 8.5 cm instead of 8 cm

find the actual error if the radius was actually 7.5 cm instead of 8 cm.

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