Q1:jipmat 2025QA › QuadrilateralsMediumQA · MCQ

From the four corners of a rectangular sheet of dimensions 25 cm x 20 cm, square of side 2 cm is cut off from four corners and a box is made. The volume of the box is:

• A$828\text{ cm}^3$
• B$672\text{ cm}^3$
• C$500\text{ cm}^3$
• D$1000\text{ cm}^3$

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The Setup: Imagine we're Minecrafting an open box out of a 2D sheet. By cutting squares out of the corners and folding the flaps up, we create a 3D cuboid. The side length of the cut square automatically becomes the height of our new box. Step 1: Determine the dimensions of the box's base. The original length is $25\text{ cm}$. Cutting $2\text{ cm}$ from *both* ends leaves a new length: $$L=25-2(2)=25-4=21\text{ cm}$$ The original width is $20\text{ cm}$. Cutting $2\text{ cm}$ from *both* ends leaves a new width: $$W=20-2(2)=20-4=16\text{ cm}$$ Step 2: Identify the height. The flaps we fold up are exactly the length of the square's side, so $H=2\text{ cm}$. Step 3: Calculate the volume of the cuboid ($V=L \times W \times H$). $$V=21 \times 16 \times 2$$ $$V=336 \times 2=672\text{ cm}^3$$ Final Answer: 672