Question

The radius of a spherical ball is 10.4 +/- 0.4 cm.
Select the correct alternative.
(1) The percentage error in radius is 3.8%
(2) The percentage error in radius is 0.4%
(3) The percentage error in volume is 11.5%
(4) The absolute error in volume is 1.2 cm3

*WITH PROPER EXPLANATION PLEASE*​

Answer 1

Answer:

3) 11.5%

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Answer 2

Given info  : The radius of a spherical ball is (10.4 ± 0.4) cm.

To select the correct alternative(s) ..

1. The percentage error in radius is 3.8%
2. The percentage error in radius is 0.4%
3. The percentage error in volume is 11.5%
4. The absolute error in volume is 1.2 cm³

solution : the percentage error in the radius = fractional error × 100

= Δr/r ×100

here , Δr = 0.4 and r = 10.4

so the percentage error in the radius = 0.4/10.4 × 100 = 400/104 ≈ 3.8% %

therefore the correct option is (1) the percentage error in radius is 3.8 %.

volume of spherical ball, V = $\frac{4}{3}\pi r^3$ = $\frac{4}{3}\pi (10.4)^3$ = 4711.82 cm³

to find error in volume,

                         $\frac{\Delta V}{V}=3\frac{\Delta r}{r}$

⇒ $\Delta V = 3\frac{\Delta r}{r}\times V$

⇒ ΔV = 3 (0.4/10.4) × 4711.82 cm³

⇒ ΔV = 543.67 cm³

the absolute error in volume is 543.67 cm³ .

and the percentage error in volume = 3 × percentage error in radius

= 3 × 3.8 = 11.4 %

therefore the percentage error in volume is 11.5 % (approx). so the correct option is (3).

hence, options (1) and (3) are correct.