The sum of length, breadth and depth of a cuboid is 18 cm and the length of its diagonal is 12 cm. Find the total surface area of the cuboid.
Answers
Answered by
2
Given, l+b+h=19cm
Length of the diagonal of cube =
l
2
+b
2
+h
2
Given, length of the diagonal =11cm
l
2
+b
2
+c
2
=11cm
=>l
2
+b
2
+c
2
=11
2
=121
=>(l+b+h)
2
−2(lb+bh+lh)=121
=>19
2
−2(lb+bh+lh)=121
=>2(lb+bh+lh)=240
But 2(lb+bh+lh) is the total surface area of the cuboid.
Hence, total surface area of the cuboid =240cm
2
Answered by
7
Step-by-step explanation:
Given, l+b+h=19cm
Length of the diagonal of cube =
l
2
+b
2
+h
2
Given, length of the diagonal =11cm
l
2
+b
2
+c
2
=11cm
=>l
2
+b
2
+c
2
=11
2
=121
=>(l+b+h)
2
−2(lb+bh+lh)=121
=>19
2
−2(lb+bh+lh)=121
=>2(lb+bh+lh)=240
But 2(lb+bh+lh) is the total surface area of the cuboid.
Hence, total surface area of the cuboid =240cm
2
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