Question

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

Answer 1

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.`