If A varies as r^2 and V varies as r^3 find percentage increase in A and V if r is increased by 20%


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Question Number 209630 by otchereabdullai@gmail.com last updated on 16/Jul/24

$I f A v a r i e s a s r^{2} a n d V v a r i e s a s r^{3}$ $f i n d p e r c e n t a g e i n c r e a s e i n A a n d V$ $i f r i s i n c r e a s e d b y 20 %$
	Answered by som(math1967) last updated on 17/Jul/24

	$A \propto r^{2} \Rightarrow A = {k r}^{2} [k v a r i a t i o n c o n s t a n t]$ $A_{i n c r e a s e} = k {(1.2 r)}^{2} = 1.44 {k r}^{2}$ $% I n c r e a s e i n A = \frac{1.44 {k r}^{2} - {k r}^{2}}{{k r}^{2}} \times 100$ $= \frac{. 44 {k r}^{2}}{{k r}^{2}} \times 100 = 44 %$ $V \propto r^{3} \Rightarrow V = {K r}^{3} [K v a r i a t i o n c o n s t a n t]$ $V_{i n c r e a s e} = K \times {(1.2 r)}^{3} = K \times 1.728 r^{3}$ $% I n c r e a s e = \frac{1.728 {K r}^{3} - {K r}^{3}}{{K r}^{3}} \times 100$ $= 72 . 8 %$
	Commented by otchereabdullai@gmail.com last updated on 17/Jul/24

	$t h a n k y o u s i r!$
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