Volume of a sphere is given by V=4/3πr³ , where r is its radius . If radius changes by 1.2% , then find the change in the volume ?

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Answer 1 · 2018-06-27T14:13:48

Volume goes with the cube of linear scaling.

#1.012^3=1.036433728,# so volume increases about #3.64%.#

Answer 2 · 2018-06-27T14:17:31

The change in volume is proportional to the original volume and approximately equal to #0.0364 * "Initial Volume"#.

Let #V_"new"# be the volume of the new sphere of the radius change and let #r_"new"# be the new radius.

#r_"new" = r+1.2%"of "r=r+1.2/100 r=r(1+1.2/100)=101.2/100r#

#V_"new" = (4pir_"new"^3)/3=(4pi(101.2/100)^3r^3)/3=(101.2/100)^3 (4pir^3)/3#

#V_"new" = (101.2/100)^3 V#

#"Change" = V_"new" - V = V[(101.2/100)^3-1]~~0.0364V#