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
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #36799)