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The lengths of three unequal edges of a rectangular solids block are in GP . if the volume of the block is `216 cm^(3)` and the total surface area is `252cm ^(2)` then the length of the longest edge isA. 12cmB. 6 cmC. 18 cmD. 3 cm |
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Answer» Correct Answer - A Let the length breadth and hight of rectangular solids block is `(a)/( r) ` a and ar respectively `therefore "volume " =(a)/( r) xxaxxar =216 cm^(3)` `implies a^(3) =216implies a^(3)=6^(3)` `therefore a=6` surface area ` =2((a^(2))/(r )+a^(2)r+a^(2))=252` `implies 2a^(2)((1)/( r) _r+1)=252` ` implies 2xx36((1+r^(2)+r)/(r ))=252` `implies (1+r^(2)+r)/(r ) =(252)/(2xx36)` `implies 1+r^(2)+r=(126)/(36rimplies 1+r^(2)+r=(21)/(6)r` `implies 6+6r^(2)=21rimplies 6r^(2)-15r+6=0` `therefore r(1)/(2),2` For ` r=(1)/(2) : "length"=(a)/(r)=(6xx2)/(1)=12` Breadth `=a=6` Height `=ar=6xx(1)/(2) =3` for r=2 : length `=(a)/(r ) =(6)/(2)=3` Breadth `=a=6` height `=ar=6xx2=12` |
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