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-

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!