Question : If the sum of the dimensions of a rectangular parallelepiped is 24 cm and the length of the diagonal is 15 cm, then the total surface area is:
Option 1: 420 cm2
Option 2: 275 cm2
Option 3: 351 cm2
Option 4: 378 cm2
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Correct Answer: 351 cm2
Solution : Let length = $a$ cm, breadth = $b$ cm , height = $c$ cm The sum of the dimensions of a rectangular parallelepiped = 24 cm ⇒ $a+b+c$ = 24 cm Diagonal = 15 cm ⇒ $\sqrt{a^{2}+b^{2}+c^{2}}$ = 15 cm ⇒ $a^{2}+b^{2}+c^{2}$ = 225 cm $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$ ⇒ 576 = 225 + $2(ab+bc+ca)$ Total surface area = $2(ab+bc+ca)$ = 576 – 225 = 351 cm2 Hence, the correct answer is 351 cm2.
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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 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 : A right pyramid stands on a square base of diagonal $10\sqrt2$ cm. If the height of the pyramid is 12 cm, the area (in cm2) of its slant surface is:
Option 1: 520 cm2
Option 2: 420 cm2
Option 3: 360 cm2
Option 4: 260 cm2
Question : The difference between the total surface area and the lateral surface area of a cube of side 12 cm is:
Option 1: 292 cm2
Option 2: 290 cm2
Option 3: 288 cm2
Option 4: 286 cm2
Question : If the volume of a cube is 1728 cm3, then what is the total surface area of the cube?
Option 1: 804 cm2
Option 2: 729 cm2
Option 3: 864 cm2
Option 4: 926 cm2
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