What is wron with my answer? Please solve this one. (a) The volume V of a growin

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What is wron with my answer?

Please solve this one.

(a) The volume V of a growing spherical cell is V=4 , where the radius is measured in micrometers (1 m = 10-6m). Find the average rate of change of V with respect to r when r changes from 3 to each of the following. (Round your answers to one decimal place.) (i) 3 to 6 um 339.2 (ii) 3 to 4 um 87.9 3 to 3.1 m (iii) 7.6 (b) Find the instantaneous rate of change of V with respect to r when r = 3 m (Round your answer to one decimal place. Need Help? Read lt 1 |Chat About ll

Explanation / Answer

Solution:   Given V = (4/3)••R³
(1)

R1 = 3 µm. & R2 = 6 µm
V1 = (4/3)••R1³ = (4/3)••3³ = 36 µ³m³
V2 = (4/3)••R2³ = (4/3)••6³ = 288 µ³m³

V/R = (V2 - V1) / (R2 - R1)
V/R =[(288 - 36) / ( 6 - 3 )
V/R =[(252) / (3)]
V/R = 84 µ²m² or
V/R = 263.76 µ²m²

(2)

R1 = 3 µm. & R2 = 4 µm
V1 = (4/3)••R1³ = (4/3)••3³ = 36 µ³m³
V2 = (4/3)••R2³ = (4/3)••4³ = (256/3)* µ³m³

V/R = (V2 - V1) / (R2 - R1)
V/R =[((256/3) - 36) / ( 4 - 3 )
V/R = (49.33)
V/R = 154.90 µ²m²

(3)

R1 = 3 µm. & R2 = 3.1 µm
V1 = (4/3)••R1³ = (4/3)••3³ = 36 µ³m³
V2 = (4/3)••R2³ = (4/3)••(3.1)³ = 39.72 µ³m³

V/R = (V2 - V1) / (R2 - R1)
V/R =[(39.721 - 36) / ( 3.1 - 3 )
V/R =[(3.721) / (0.1)]
V/R = 37.21 µ²m² or
V/R = 116.85 µ²m²

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