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113. A rectangular metallic sheet haslength 48 cm and breadth 36 cm.From each of the vertices of it, asquare sheet of side 8 cm is cut offand an open box is made from theremaining part of the sheet. What isthe volume of the box formed incubic cm ? |
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Answer» The answer is 650cm3 I Don't Know This Type Of Questions It is given that a box is to be made by a rectangular sheet of tin of side 35 cm by 24 cm. Let the side of the box that have to be cut isxcmx cm. Length of the box after cutting will be45−x−x45−x−xor45−2x45−2x. Breadth of the box after cutting will be24−x−x24−x−xor24−2x24−2x. Height will remain same that isxx. Let,V(x)V(x)be the volume of the box. V(x)=length×breadth×height=(45−2x)(24−2x)(x)=x(1080−90x−48x+4x2)=4x3−138x2+1080xV(x)=length×breadth×height=(45−2x)(24−2x)(x)=x(1080−90x−48x+4x2)=4x3−138x2+1080x Differentiate the function with respect tox, The box will have the following dimensions:-Length=(48-8-8) = 32 cmBreadth=(36-8-8)= 20 cmHeight= 8 cmVolume of the box formed=32×20×8 =5120cm3This is your required answer length=(48-8-8)=32 cm, breadth =(36-8-8)=20 cm, Height = 8 cm Volume = 32 x 20x8= 32 x 160=5120 cm^3 |
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