Question : If the surface area of a cube is 5046 cm2, then the volume of the cube is:
Option 1: 26189 cm3
Option 2: 25145 cm3
Option 3: 22812 cm3
Option 4: 24389 cm3
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Correct Answer: 24389 cm3
Solution : Given: The surface area of a cube is 5046 cm2. The surface area of a cube is given by $6a^2$, where $a$ is the length of a side. $a = \sqrt{\frac{5046}{6}} = 29$ cm The volume $(V)$ of a cube is given by $a^3$. $V = a^3 = (29)^3 = 24389$ cm3 Hence, the correct answer is 24389 cm3.
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Question : The volume of a cylinder is 4312 cm3. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm2) is: (Take $\pi=\frac{22}{7}$ )
Option 1: 572 cm2
Option 2: 528 cm2
Option 3: 660 cm2
Option 4: 616 cm2
Question : If the length of the diagonal of a cube is $7 \sqrt{3} \mathrm{~cm}$, then the surface area of the cube is_____.
Option 1: 216 cm2
Option 2: 256 cm2
Option 3: 284 cm2
Option 4: 294 cm2
Question : The volume of a solid hemisphere is 19404 cm3. Its total surface area is:
Option 1: 4158 cm2
Option 2: 2858 cm2
Option 3: 1738 cm2
Option 4: 2038 cm2
Question : The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm2. If the radius of its base is 7 cm, then what is the volume of this cylinder? (use $\pi=\frac{22}{7}$)
Option 1: 2060 cm3
Option 2: 2480 cm3
Option 3: 3080 cm3
Option 4: 2760 cm3
Question : Three cubes of equal volume are joined end to end. Find the surface area of the resulting cuboid if the diagonal of the cube is $6 \sqrt{3} \mathrm{~cm}$.
Option 1: 509 cm2
Option 2: 504 cm2
Option 3: 516 cm2
Option 4: 512 cm2
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