Question : The length of the longest diagonal that can be placed in a closed cube is $50 \sqrt{3}$ cm. What is the total surface area of this cube?
Option 1: 15000 cm2
Option 2: 10000 cm2
Option 3: 12000 cm2
Option 4: 6000 cm2
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Correct Answer: 15000 cm2
Solution : Let $a$ be the side of the cube. The length of the longest diagonal that can be placed in a closed cube = $50 \sqrt{3}$ cm $⇒\sqrt3 a=50 \sqrt{3}$ $\therefore a = 50$ cm Total surface area = $6a^2= 6 × 50 × 50= 15000$ cm2 Hence, the correct answer is 15000 cm2.
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Question : The total surface area of a closed cube is 128 cm2 more than the area of a square. If the length of each side of the cube is 8 cm, then what is the length of each side of the square?
Option 1: 16 cm
Option 2: 12 cm
Option 3: 18 cm
Option 4: 9 cm
Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:
Option 1: 256 cm2
Option 2: 265 cm2
Option 3: 315 cm2
Option 4: 351 cm2
Question : If the volume of a cube is 5832 cm3, then what is the lateral surface area of this cube?
Option 1: 1024 cm2
Option 2: 384 cm2
Option 3: 576 cm2
Option 4: 1296 cm2
Question : The length of each diagonal of a rectangle is 50 cm. If its breadth is 14 cm, then what will be the area of the rectangle?
Option 1: 832 cm2
Option 2: 716 cm2
Option 3: 784 cm2
Option 4: 672 cm2
Question : If the area of a square is 529 cm2, then what is the length of its diagonal?
Option 1: $23\mathrm{~cm}$
Option 2: $26 \sqrt{3} \mathrm{~cm}$
Option 3: $23 \sqrt{2 } \mathrm{~cm}$
Option 4: $46 \mathrm{~cm}$
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