Question 62

The radius of a sphere is reduced by 40%. By what percent will its volume decrease?

Solution

Volume of sphere = $$\frac{4}{3}\pi\ r^3$$

So radius is reduced by 40%

Net change =$$+x+y+\frac{\left(x\times\ y\right)}{100}$$

Area will decreased by = $$-40-40+\frac{\left(-40\times\ -40\right)}{100}=-80+16=-64\%$$

Now volume will decreased by = $$-64-40+\frac{\left(-64\times\ -40\right)}{100}=-104+25.6=-78.4\%$$

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