Question

Solve the numerical example.

The diameter of a sphere is 2.14 cm. Calculate the volume of the sphere to the correct number of significant figures.

Answer 1

Volume of sphere =`4/3 pi"r"^3`

`= 4/3 xx 3.142 xx (2.14/2)^3`     ...`(because "r" = "d"/2)`

`= 4/3 xx 3.142 xx (1.07)^3`

= 1.333 × 3.142 × (1.07)³

= {antilog [log (1.333) + log(3.142) + 3 log(1.07)]}

= {antilog [0.1249 + 0.4972 + 3 (0.0294)]}

= {antilog [0.1249 + 0.4972 + 3 (0.0294)]}

= {antilog [0.6221 + 0.0882]}

= {antilog [0.7103]}

= 5.133cm³ 

In multiplication or division, the final result should retain as many significant figures as there are in the original number with the least significant figures.

∴ Volume in correct significant figures = 5.13 cm³