The volume of a cuboid is 54cm 3 . If the length, width and height
MATHEMATICS
WAEC 2012
The volume of a cuboid is 54cm3. If the length, width and height of the cuboid are in the ratio 2:1:1 respectively, find its total surface area
- A. 108cm2
- B. 90cm2
- C. 80cm2
- D. 72cm2
Correct Answer: B. 90cm2
Explanation
V = L x B x H
V = \(2x \times x \times x = 2x^3\)
= 54cm3
i.e. 2x3 = 54
x3 = \(\frac{54}{2}\) = 27
x = 3\(\sqrt{27}\)
x = 3
L = 2x i.e. 2 x 3 = 6cm
B = x i.e. x = 3cm
H = x i.e. x = 3cm
but A = 2(LB + LH + BH) = 2(6 x 3) + (6 x 3) + (3 x 3) = 2(18 + 18 + 9) = 2(45)
= 90cm2
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