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in Differentiation by (28.7k points)
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A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is

A. 12000π mm3

B. 800π mm3

C. 80000π mm3

D. 120π mm3

2 Answers

+2 votes
by (29.1k points)
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Best answer

Correct answer is C.

We know that volume of sphere = v = (4/3) × πr3 (r is radius of sphere)

r = 100mm

+2 votes
by (105 points)

\(V=\frac43\pi r^3\\\text{If }r_1= 100mm\text{ and }r_2 = 98mm,\text{ then:}\\V_1=\frac43\pi10^6mm\text{ and } \\V_2=\frac43\pi(100-2)^3mm\\=\frac43\pi(10^6-8-600\cdot98)\\\text{Therefore:}\\V_1-V_2=\frac43\pi(8+6\times10^4-1200)\\\approx 80000\pi \space mm^3\)

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