Question : The sum of the length, breadth, and height of a cuboid is 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of the cuboid.
Option 1: 364 cm2
Option 2: 256 cm2
Option 3: 356 cm2
Option 4: 264 cm2
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Correct Answer: 256 cm2
Solution : Given: The sum of the length, breadth, and height of a cuboid is 20 cm. The length of the diagonal is 12 cm. Use the formulas, The length of the diagonal of the cuboid = $\sqrt{l^2+b^2+h^2}$, The total surface area of the cuboid = $2(lb+bh+lh)$, where $l$, $b$, and $h$ are the length, breadth, and height respectively. According to the question, $\sqrt{l^2+b^2+h^2}=12$ ⇒ $l^2+b^2+h^2=144$ (equation 1) Also, $(l+b+h)=20$ (equation 2) Squaring both sides of the equation 2, $(l+b+h)^2=(20)^2$ ⇒ $l^2+b^2+h^2+2(lb+bh+lh)=400$ Substitute the value of $l^2+b^2+h^2$ from the equation 1, ⇒ $144+2(lb+bh+lh)=400$ ⇒ $2(lb+bh+lh)=400–144$ ⇒ $2(lb+bh+lh)=256$ cm2 Hence, the correct answer is 256 cm2.
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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 3: 284 cm2
Option 4: 294 cm2
Question : Volume of a cuboid is 4,800 cm3. If the height of this cuboid is 20 cm, then what will be the area of the base of the cuboid?
Option 1: 150 cm2
Option 2: 240 cm2
Option 3: 480 cm2
Option 4: 120 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
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
Question : The base of a right prism is a square having a side of 15 cm. If its height is 8 cm, then find the total surface area.
Option 1: 940 cm2
Option 2: 920 cm2
Option 3: 900 cm2
Option 4: 930 cm2
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