The volume of a cube is four times the volume of a cuboid. If the sides of the cuboid are 32 cm, 8 cm and 4 cm, then find the ratio of the total surface area of the cube to that of the cuboid.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 24 : 13.
Length of the cuboid = 32 cm
Breadth of the cuboid = 8 cm
Height of the cuboid = 4 cm
According to the question -
⇒ Volume of the cube = 4 × Volume of the cuboid
⇒ side3 = 4 × (length × breadth × height)
⇒ side3 = 4 × (32 × 8 × 4)
⇒ side3 = 4096
⇒ side = 16
Total surface area of the cube = 6(side)2 = 6(16)2 = 1536 cm2
Total surface area of the cuboid = 2 [(length × breadth) + (breadth × height) + (length × height)] = 2 [(32 × 8) + (8 × 4) + (4 × 32)] = 2 [256 + 32 + 128] = 2(416) = 832 cm2
Total surface area of the cube/Total surface area of the cuboid = 1536/832 = 24 : 13