[填空题]
The density of a soli u-1o) xcohpe3d sphere is measuci i,25vxhjx;hj8k.zple 7p4 red with percentage uncertainty of 5%. The radius of thjii 4xxkpjhh ;ep,z8v c5 .27le sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass of the sphere? % (Please do not include the % simbol in the blank)
参考答案: 20.0
本题详细解析: The mass of the sphere can be calculated by mu;(cjhkxo x0x(db 3(a*3ohkr f0a1rbwltiplying its volume by the density ojko0fxrk1b0rhd w(; (hc*3(ba xx3aof the material of which it is made: $$M=\frac{4}{3} \pi r^3 \rho$$ so the percentage uncertainty in $M$ is $$\frac{\Delta M}{M}=3 \frac{\Delta r}{r}+\frac{\Delta \rho}{\rho} .$$ The percentage uncertainty in $r$ is $5 \%$, so the percentage error in $M$ is $(3 \times 5 \%)+5 \%=20 \%$
