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प्रश्न
If V = pr2h and S = 2pr2 + 2prh, then express V in terms of S, p and r.
उत्तर
V = πr2h and S = 2πr2 + 2πrh
S = 2πr2 + 2πrh
⇒ 2rh = S - 2πr2
⇒ h = `("S" - 2pi"r"^2)/(2pi"r")`
Substitute h in V = πr2h
⇒ V = `pi"r"^2(("S" - 2pi"r"^2)/(2pi"r"))`
⇒ V = `"r"(("S" - 2pi"r"^2)/(2))`
⇒ V = `"Sr"/(2) - pi"r"^3`.
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