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Question Number 100341 by peter frank last updated on 26/Jun/20
Anopenboxwithasquarebaseistobemadeoutofagivenquantityofacardboardofareac2squareunits.showthemaximumvolumeoftheboxc263cubicunits
Commented by PRITHWISH SEN 2 last updated on 26/Jun/20
Lettheareaofthefloor=x2theareaoftheremaining4sides=c2−x2∴theheightoftbebox=c2−x24x∴Thevol.V(x)=14(c2−x2)xV′(x)=14(c2−3x2)=0⇒x2=c23V″(x)=−32x<0∀x∴Vmax.=14(c2−c23)c3=c363proved.
Answered by bobhans last updated on 26/Jun/20
volumeofthebox=V(x)=(c−2x)2xV′(x)=(c−2x)2−4(c−2x)x=0(c−2x){c−2x−4x}=0,x=16cVmax=(c−13c)2.(16c)=(4c29)(c6)=2c327◼
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