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(a)
Width of the rectangular base = x cm
Length of the rectangular base = 3x cm
Height = h cm

Total surface area in cm²:
2 (x•3x + x•h + 3x•h) = 250
3x² + 4xh = 125
4xh = 125 - 3x²
h = (125 - 3x²)/(4x)

Volume of the cuboid, V cm³
= 3x•x•h cm³
= 3x²•(125 - 3x²)/4x cm³
= 3x(125 - 3x²)/4 cm³

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(b)
(i)
The cylinder and each inscribed cylinder are similar.
Hence, r/h = 9/15
h = (5/3)r

Volume of the cylinder, V cm³
= π•r²•h cm³
= π•r²•(5/3)r cm³
= 5πr³/3 cm³

(ii)
The cylinder and each inscribed cylinder are similar.
Hence, r/h = 9/15
r = 3h/5

Volume of the cylinder, V cm³
= π•r²•h cm³
= π•(3h/5)²•h cm³
= 9πh³/25 cm³