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A storage box is a cuboid. One corner is at the origin…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A storage box is a cuboid. One corner is at the origin. Its three edges from that corner run along the positive $x$ -axis, the positive $y$ -axis and the positive $z$ -axis, and they are $4\ \text{m}$ , $5\ \text{m}$ and $3\ \text{m}$ long. The box has eight corners. Count how many corners lie on at least one coordinate plane, including the origin. Then count how many corners lie on an axis, not counting the origin.

A storage box shaped like a cuboid with one corner at the origin O and three edges along the positive axes, 4 units along x, 5 units along y and 3 units along z. All eight corners are labelled with their coordinates. The corner (4, 5, 3) is marked in red because it is the only corner with no zero coordinate.

Need a reminder? The key ideaShow

The three signs of $(x, y, z)$ decide the octant. A point on an axis has two zero coordinates, and a point in a coordinate plane has one. The distance of $P$ from the $xy$ -plane is $|z|$ , from the $yz$ -plane $|x|$ and from the $zx$ -plane $|y|$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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