How do I simplify:
\[ S = 2\pi r^2 + 2\pi rh \]
Then, how do I make \( h \) the subject?
What is the value of \( h \) if \( S = 50 \) and \( r = 3 \)?
Answer (2)
S = 2 π r 2 + 2 π r h 2 π r h + 2 π r 2 = S ∣ s u b t r a c t 2 π r 2 f ro m b o t h s i d es 2 π r h = S − 2 π r 2 ∣ d i v i d e b o t h s i d es b y 2 π r h = 2 π r S − 2 π r 2 S = 50 ; r = 3 h = 2 π ⋅ 3 50 − 2 π ⋅ 3 2 = 6 π 50 − 2 π ⋅ 9 = 6 π 50 − 18 π < 0 − n o se n se I t hink ... S n o t e q u a l 50 !!!
To simplify S = 2 π r 2 + 2 π r h , factor it as S = 2 π ( r 2 + r h ) and isolate h using h = 2 π r S − 2 π r 2 . For S = 50 and r = 3 , the calculation shows h may be negative, which is not valid in this context. Hence, a positive value for h cannot be obtained with these inputs.
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