Question : A solid cube has a side of 8 cm. It is cut along diagonals of the top face to get 4 equal parts. What is the total surface area (in cm2) of each part?
Option 1: $96 + 64\sqrt2$
Option 2: $80 + 64\sqrt2$
Option 3: $96 + 48\sqrt2$
Option 4: $80 + 48\sqrt2$
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Correct Answer: $96 + 64\sqrt2$
Solution : Diagonal of the face = (side of cube) × $\sqrt{2} = 8\sqrt{2}$ cm The total surface area of the part = Area of one face of cube + 2 × $\frac{1}{4}$ × area of top face + 2 × side of cube × $\frac{1}{2}$ × diagonal of face = $8 × 8 + \frac{1}{2} × 64 + 2 × 8 × \frac{1}{2} × 8\sqrt2$ = $64 + 32 + 64\sqrt2$ = $96 + 64\sqrt2$ cm2 Hence, the correct answer is $96 + 64\sqrt2$.
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Question : The curved surface area of a solid hemisphere is 22 cm2. What is the total surface area of the hemisphere? (use $\pi=\frac{22}{7}$)
Option 1: 66 cm2
Option 2: 44 cm2
Option 3: 33 cm2
Option 4: 30 cm2
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
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 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
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