17. The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal 11 cm. The total surface area of the cuboid is (1) 140 cm2 (2) 240 cm2 (3) 250 cm2 (4) 245 cm2
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The sum of length, breadth and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the area of cuboid.
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Length of diagonal of cuboid =
l
2
+b
2
+c
2
Surface area of cuboid =2(lb+bh+hl)
Assume -
⇒length=l
Breadth=b
Depth=h
Given eq (1) l+b+h=19
eq (2) length of diagonal =11
⇒
l
2
+b
2
+h
2
=11
Simplifying eq (2)
⇒l
2
+b
2
+h
2
=121
Taking (l+b+h)
2
=l
2
+b
2
+h
2
+2lb+2bh+2lh
substituting values
⇒(19)
2
=121+2(lb+bh+lh)
⇒361−121=2(lb+bh+lh)
⇒240=2(lb+bh+lh)
∴ Surface area of cuboid =240
Answer:
Answer: Surface area of the cuboid 240 square cm.
Step-by-step explanation:
Surface area of cuboid =2(lb+bh+hl)
Assume -
⇒length=l
Breadth=b
Depth=h
Given eq (1) l+b+h=19
eq (2) length of diagonal =11
substituting values
⇒(19)
2
=121+2(lb+bh+lh)
⇒361−121=2(lb+bh+lh)
⇒240=2(lb+bh+lh)
∴ Surface area of cuboid =240.