A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is molted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes?
A. 4 : 7
B. 7 : 8
C. 7 : 12
D. 2 : 3
Answer: Option B
Solution (By Examveda Team)
Let the side of new cube is x cmVolume of cuboid = 8 x volume of new cube
18 × 36 × 72 = 8x3
18 × 18 × 18 = x3
x = 18 cm
$$\eqalign{ & \frac{{{\text{Total surface area of cuboid}}}}{{8 \times {\text{Curved surface area of cube}}}} \cr & = \frac{{2\left( {lb + bh + hl} \right)}}{{8 \times 4{x^3}}} \cr & = \frac{7}{8} \cr} $$
This Question Belongs to Arithmetic Ability >> Mensuration 3D
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A sphere and a hemisphere have the same volume. The ratio of their curved surface area is:
A. $${2^{\frac{3}{2}}}:1$$
B. $${2^{\frac{2}{3}}}:1$$
C. $${4^{\frac{2}{3}}}:1$$
D. $${2^{\frac{1}{3}}}:1$$
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