Question : A cuboid with sides 4, 6, and 8 units is covered with paper. The paper is removed and a square is made from it. What is the side (in units) of the square?
Option 1: 12.24
Option 2: 16.62
Option 3: 14.42
Option 4: 12.62
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Correct Answer: 14.42
Solution : The total surface area of cuboid $= 2(lb+bh+hl)$ where $l$ is the length, $b$ is the breadth, and $h$ is the height of the cuboid. Area of square = $(\text{side})^2$ According to the question, The paper used for covering the cuboid is removed and a square is made. So, the total surface area of the cuboid = Area of the square ⇒ $2(lb+bh+hl) = (\text{side})^2$ ⇒ $2(4\times 6 +6\times 8+8\times 4)=(\text{side})^2$ ⇒ $2(24+48+32)=(\text{side})^2$ ⇒ $2(104)= (\text{side})^2$ ⇒ $\text{side}=\sqrt{208}=14.42\ \mathrm{cm}$ Hence, the correct answer is 14.42.
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Question : The area of triangle formed by the straight line $3x + 2y = 6$ and the co-ordinate axes is:
Option 1: 3 square units
Option 2: 6 square units
Option 3: 4 square units
Option 4: 8 square units
Question : A conical tent with a radius of 6 units and a height of 8 units is to be made with canvas. How much canvas is needed to make the tent? (Rounded off to two places of decimals)
Option 1: 188.57 units
Option 2: 155.87 units
Option 3: 166.57 units
Option 4: 177.55 units
Question : If the side of a square is $\frac{1}{2}(x+1)$ units and its diagonal is $\frac{3-x}{\sqrt{2}}$ units, then the length of the side of the square would be:
Option 1: $\frac{4}{3}$ units
Option 2: $\frac{1}{2}$ unit
Option 3: 1 unit
Option 4: 2 units
Question : The midpoints of sides AB and AC of the triangle ABC are, respectively, X and Y. If (BC + XY) = 12 units, then the value of (BC – XY) is:
Option 1: 2 units
Option 2: 6 units
Option 3: 8 units
Option 4: 4 units
Question : The area of triangle with vertices A(0, 8), O(0, 0), and B(5, 0) is:
Option 1: 8 sq. units
Option 2: 13 sq. units
Option 3: 20 sq. units
Option 4: 40 sq. units
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