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What are the values for x and y of a cuboid whose dimensions are x cm by y cm by 4 cm having a volume of 135 cubic cm and a surface area of 163.5 square cm?
Wiki User
∙ 10y ago
Volume = length x width x depth = 4xy cm3 = 135 cm3 [1]
Surface area = 2 x (length x width + length x depth + width x depth)
= 2 x (xy + 4x + 4y) cm2 = 163.5 cm2 [2]
From [1]: 4xy = 135 → y = 135/4x
Substituting in [2]:
2(xy + 4x + 4y) = 163.5
→ 2(x(135/4x) + 4x + 4(135/4x)) = 163.5
→ 135/2 + 8x + 270/x = 327/2
→ -96 + 8x + 270/x = 0
→ 4x2 - 48x + 135 = 0
→ (2x - 15)(2x - 9) = 0
→ x = 7.5 or 4.5
→ y = 4.5 or 7.5 (respectively).
Thus the cuboid is 7.5 cm by 4.5 cm by 4 cm.
Wiki User
∙ 10y ago
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