Question : The length, breadth, and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface of the cuboid is:
Option 1: 216 cm2
Option 2: 324 cm2
Option 3: 432 cm2
Option 4: 460 cm2
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Correct Answer: 432 cm2
Solution : Volume of cuboid = 576 cm2 The ratio of length, breadth, and height of a cuboid = 3 : 4 : 6 Let the length, $l$ = $3x$, breadth, $b$ = $4x$, and height, $h$ = $6x$. Volume of cuboid = $l×b×h$ = $3x×4x×6x$ ⇒ 576 = 72$x^{3}$ ⇒ $x^{3}$ = 8 ⇒ $x$ = 2 So, $l$ = $3x$ = 6 cm $b$ = $4x$ = 8 cm $h$ = $6x$ = 12 cm Total surface area = $2(lb+bh+hl)$ = 2 × (6 × 8 + 8 × 12 + 12 × 6) = 2 × (48 + 96 + 72) = 432 cm2 Hence, the correct answer is 432 cm2.
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Question : The sum of the length and breadth of a cuboid is 4 cm. Length is three times the breadth. If the height of the cuboid is half of the sum of its length and breadth. Then what is the total surface area of the cuboid?
Option 1: 64 cm2
Option 2: 22 cm2
Option 3: 32 cm2
Option 4: 30 cm2
Question : The length of a cuboid is thrice of its breadth and the height of a cuboid is twice its breadth. If the breadth of the cuboid is 6 cm, then what is the total surface area of the cuboid?
Option 1: 844 cm2
Option 2: 708 cm2
Option 3: 762 cm2
Option 4: 792 cm2
Question : The length of a cuboid is 8 cm. If the breadth of the cuboid is twice its length and the height of the cuboid is half of its length, then what is the total surface area of the cuboid?
Option 1: $448 \ \text{cm}^2$
Option 2: $216 \ \text{cm}^2$
Option 3: $188\ \text{cm}^2$
Option 4: $154\ \text{cm}^2$
Question : A square of side 3 cm is cut off from each corner of a rectangular sheet of length 24 cm and breadth 18 cm, and the remaining sheet is folded to form an open rectangular box. The surface area of the box is:
Option 1: 468 cm2
Option 2: 396 cm2
Option 3: 612 cm2
Option 4: 423 cm2
Question : The sum of the length, breadth, and height of a cuboid box is 20 cm and the total surface area of a cuboid is 256 sq. cm. What is the maximum length (in approximate) of a stick that can be placed inside the cuboid box?
Option 1: 16 cm
Option 2: 24 cm
Option 3: 32 cm
Option 4: 12 cm
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