Question

SHOW AU WORK! 3 MHE SURFACE AREA OF A SPHERE IS S = 4012 IF THE RHOIUS OF THE SPHERE IS MGASUNED 70 se 3.95 cm AND IT IS ACIVALY 405cm a) Flvo ennOR W RADIUS 4 = b) FIND RE, c) Fuo Per d) FWD EXACT Ennek W SURFACE AROM AS = e) Fus pornol. Ennor W ANFACE ANGA ds= f) FIND RES USING d) RES g) FIND Pts h) FIND PROPOGADOW FARK

Answer 1

ANSWER:-

The surface area of a sphere is s=

4л

Here,Given that the actual value of the radius ,
ТА = 4.05cm
and the measured value of the radius is

a) So, the error in radius

Ar=rA-IM

=> Ar= (4.05 – 3.95) cm

$\Rightarrow \Delta r=0.1\,cm$

b) Now, The relative error;

$R\epsilon _r=\frac{\Delta r}{r_A}$

$\Rightarrow R\epsilon _r=\frac{0.1}{4.05}$

$\Rightarrow R\epsilon _r=0.025(approx)$

c) Now, The percentage error,

$P\epsilon _r=\frac{\Delta r}{r_A}\times100$%

$\Rightarrow P\epsilon_r =\frac{0.1}{4.05}\times100$%

$\Rightarrow P\epsilon_r =0.025\times100$%

$\Rightarrow P\epsilon_r =2.5$% (approx)

d) Now,

$S=4\pi r^2$

So, The actual surface area,

$S_A=4\pi r^2_A$

$\Rightarrow S_A=4\times \frac{22}{7}\times (4.05)^2$

$\Rightarrow S_A=4\times \frac{22}{7}\times16.4025$

$\Rightarrow S_A=\frac{1443.42}{7}$

$\Rightarrow S_A=206.2 cm^2$

and the measured surface area

$S_M=4\pi r^2_M$

$\Rightarrow S_M=4\times\frac{22}{7}\times(3.95)^2$

$\Rightarrow S_M=4\times\frac{22}{7}\times15.6025$

$\Rightarrow S_M=\frac{1373.02}{7}$

$\Rightarrow S_M=196.16\,cm^2$

Thus, The exact error in surface area,

$\Delta S=S_A-S_M$

$\Rightarrow \Delta S=(206.2-196.16)cm^2$

$\Rightarrow \Delta S=10.04cm^2$

----------------------------------------------------------------------------------------------------------------------------------------------------------Sorry for the inconvenience 4 was solved 4 answer remaining part will solving next time .

THANK YOU.