Math, asked by varshapradeep1835, 1 year ago

The radius of a sphere is measured to be 2.1 plus minus 0.5 cm calculate surface area with error limits and its volume percentage

Answers

Answered by sanjeevk28012
5

Given :

The radius of sphere measured = ( 2.1 \pm 0.5 ) cm

To Find :

The surface area of sphere with error limits

The volume percentage of sphere

Solution :

∵ Radius of sphere measured = ( 2.1 \pm 0.5 ) cm

Surface area of sphere = A = 4 × π × radius²

                                                = 4 × 3.14 × (2.1 cm)²

                                                = 55.4 cm²

Now,

\dfrac{Change in Area}{Area} = 2 × \dfrac{Change in Radius}{Radius}

i.e  \dfrac{\Delta A}{A} =  2 × \dfrac{\Delta r}{r}

Or, ΔA = 2 × A ×  \dfrac{\Delta r}{r}

Or, ΔA = 2 × 55.4 cm² ×  \dfrac{0.5}{2.1}

∴   ΔA = 26.3 cm²

Change in surface Area = ΔA = 56.4 cm²

Surface Area with error limit = ( 55.4 \pm 26.3 ) cm²

Again

Volume of sphere = \dfrac{4}{3} ×  π × radius³

                               =  \dfrac{4}{3} ×  3.14 × ( 2.1 cm)³

                              = 38.77 cm³

Now,

\dfrac{Change in Volume}{Volume}  = 3 × \dfrac{Change in Radius}{Radius}

i.e    \dfrac{\Delta V}{V} =  3 × ( \dfrac{\Delta r}{r}

Or, ΔV = 3 × V × ( \dfrac{\Delta r}{r}

Or, ΔV = 3 × 38.77 cm³ × (  \dfrac{0.5}{2.1}

∴   ΔV = 128.23  cm³

Change in volume = ΔV =  128.23  cm³

Volume with error limit = ( 38.77 \pm 128.23 ) cm³

Hence, Surface Area with error limit is ( 55.4 \pm 26.3 ) cm²

And, Volume with error limit is ( 38.77 \pm 128.23 ) cm³   Answer

Similar questions