Respuesta :
Base area of cuboid is 540 m².
According to the statement
we have to find the base area of the cuboid.
So, For this purpose, we know that the
A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges.
From the given information:
Let the length, breadth and height of the cuboid be l, b and h respectively.
We have given that,
Breadth = ¼ × Length⇒ b = ¼ × l - - ( 1 )
Also,Height = ⅔ × Length⇒ h = ⅔ × l - - ( 2 )
We know that,Volume of cuboid = l × b × h
972 = l × ¼ × l × ⅔ × l - - [ From given]
⇒ ( 972 × 4 × 3 ) ÷ ( 1 × 2 ) = l × l × l
⇒ 972× 2 × 3 = l³
⇒ 486× 2 × 2 × 3 = l³l³
= 18 m.
Then
Now,Breadth of cuboid = ¼ × Length
⇒ b = ¼ × 18
⇒ b = 18÷ 4
⇒ b = 4.5 m.
Now,
Height of cuboid = ⅔ × Length
⇒ h = ⅔ × 18
⇒ h = ( 2 × 18 ) ÷ 3
⇒ h = 36 ÷ 3⇒ h = 12 m
.Now, we have,
Length ( l ) = 18
Breadth ( b ) = 4.5
Height ( h ) = 12
Now, we know that,
Total surface area of cuboid = 2 height(length + breadth)
⇒ Base area = 2 (12(18+ 4.5))
⇒ Base area = 2 (12(22.5))
⇒ Base area = 2 [ 270 ]
⇒ Base area = 2 × 270
⇒ Base area = 540 m².
So, Base area of cuboid is 540 m².
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