The lateral surface area and the total surface area of a cuboid are 238 centimetre square and 382 cm square if the height of the cuboid is 7 cm find the volume of the cuboid
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lateral s.a.= 2h(l+b)
238=2h(l+b)
119=h(l+b)
119/h=l+b
119/7=l+b
l+b=17.............(i)
b=17-l...........(ii)
total s.a.= 2(lb+bh+hl)
382/2=lb+bh+hl
191=l(17-l)+ h(l+b) {from (ii)}
17 l- l² +7(17) =191 {from (i)}
l² -17 l +72=0
l² -8 l -9 l +72=0
l(l-8) - 9(l-8)=0
(l-8)(l-9)=0
thus, l=9 or 8
and b=8 or 9 respectively [from (ii)]
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Answer:
L = 9 or 8
B= 8 or 9
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