Question

The radius of a sphere is measured to be (1.2 +- 0.2)cm. Calculate its volume with error limits.

Answer 1

Answer:

hola mate..

The volume is given as

V = (4/3)πr3

so,

V = (4/3) x 3.14 x 5.33

thus,

V = 623.30 cm3

now, the error equation

ΔV/V = 3(Δr/r)

or

ΔV = V x 3(Δr/r)

thus,

ΔV = 623.30 x 3x(0.1/5.3)

or error in surface area

ΔV = +/- 35.28 cm3

thus,

ΔV/V x 100 = (35.28/623.30)

so,

ΔV/V x 100 = 5.66 %

hope it helps..

Answer 2

Volume of sphere = (7.24 ± 3.6)

Given:

The radius of a sphere is measured to be (1.2 ± 0.2)cm.

To find:

Volume with error limits.

Formula used:

Volume of sphere = $\frac{4}{3}$ × $\pi$ R³

      $\frac{\Delta V}{V}=3\left(\frac{\Delta r}{r}\right)$

Where $\Delta r$ = Error in radius.

Explanation:

From given:

Volume of sphere = $\frac{4}{3}$ × $\pi$ R³

Volume of sphere = $\frac{4}{3}$ × $\pi$ × 1.2³

Volume of sphere = 7.24 cm³

$\Delta r$ = Error in radius = 0.2 cm

       $\Delta V=3\left(\frac{\Delta r}{r}\right) \times V$

       $\Delta V=3\left(\frac{0.2}{1.2}\right) \times 7.24$

       $\Delta V$ = 3.6 cm³

Volume of sphere = (7.24 ± 3.6)

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