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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Correct Answer: 864 cm2
Solution : The volume of a cube is given by the formula $V = a^3$, where $a$ is the length of a side. Given that the volume $V$ is 1728$\text{ cm}^3$, $a = \sqrt[3]{V} = \sqrt[3]{1728} = 12 \text{ cm}$ So, the total surface area $A$ of a cube, $A = 6a^2$ Substituting $a = 12$$\text{ cm}^2$, $⇒A = 6 \times (12)^2 = 6 \times 144 = 864 \text{ cm}^2$ Hence, the correct answer is 864 cm2.
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Question : If the volume of a cube is 729 cm3, then find the total surface area of the cube.
Option 1: 484 cm2
Option 2: 482 cm2
Option 3: 488 cm2
Option 4: 486 cm2
Question : If the total surface area of a cube is 96 cm2, its volume is:
Option 1: 56 cm3
Option 2: 16 cm3
Option 3: 64 cm3
Option 4: 36 cm3
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 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
Question : The total surface area of a solid hemisphere of diameter 14 cm is (use $\pi=\frac{22}{7}$ ):
Option 1: 522 cm2
Option 2: 462 cm2
Option 3: 428 cm2
Option 4: 584 cm2
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