a cuboid has a square base and is 12 cm high if its total surface area is 512 cm^2 find the area of its base
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Total surface area - 512 cm²
Height = 12 cm
Define x:
Let the length be x
Form equation:
Total surface = 2(length x length) + 4(length x height)
Total Surface area = 2x² + 4(12x) = 2x² + 48x
Solve x:
2x² + 48x= 512
2x² + 48x - 512 = 0
2(x - 8)(x + 32) = 0
x = 8 or x = -32 (rejected because length cannot be negative)
Find the length:
Length = x = 8 cm
Find the base area:
Area = Length x Length
Area = 8 x 8 = 64 cm²
Answer: The base area is 64 cm²
mathsaproblem:
but formula of surface area is 2(lh+bh+lb)
the base is a square, so the length and the breadth are the same, they are all x.
so 2(2(xh)+ x²+x²) = 4(xh) + 2x²
To check back: SA = 2 (8x12 + 8x12 + 8x8) = 512 cm²
oh
thanks once again
Well done .
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