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
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Correct Answer: 16 cm
Solution : Length of each side of the cube = 8 cm Total surface area of the cube = 6a$^2$ = area of a square + 128 cm$^2$ Let's assume that the length of each side of the square is "x" cm. Surface area of a cube = 6a$^2$ Area of a square = x$^2$ Total surface area of the cube = 6a$^2$ = 6(8$^2$) = 384 cm$^2$ Area of the square = x$^2$ According to the problem, 6a$^2$ = x$^2$ + 128 Substituting the value of 6a$^2$, we get: 384 = x$^2$ + 128 ⇒ x = $\sqrt{(384 - 128)} = \sqrt{256}$ = 16 cm Hence, the correct answer is 16 cm.
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Question : The length of each side of a square is 16 cm. What is the area of the square?
Option 1: 112 cm2
Option 2: 176 cm2
Option 3: 128 cm2
Option 4: 256 cm2
Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
Option 1: 128 cm2
Option 2: 112 cm2
Option 3: 184 cm2
Option 4: 156 cm2
Question : The length of each side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then what is the area of the rhombus?
Option 1: 108 cm2
Option 4: 96 cm2
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
Question : The length of each side of a cube is 4 cm. What is the volume of the cube?
Option 1: 128 cm3
Option 2: 48 cm3
Option 3: 64 cm3
Option 4: 32 cm3
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