Question 5. Find the height of the shapes.
Tìm chiều cao của các hình?
You got this one right too. The cylinder is 438 cm and the cube is 365 cm.
And the sum at the end was the easy part — it is the same sum you did for An and Bình's pebbles. What was hard here is that nobody handed you the two numbers. You had to get them out of the picture, and the picture gives them to you the wrong way round.
That one flip is what this whole page is about.
Forget 803 for a moment. Here is a wall 840 cm high, and some blocks that stack exactly to the top of it. Slide, and watch what happens to each block.
The more of something you need, the shorter each one must be.
Same height, more pieces → smaller pieces. Always.
It sounds obvious said out loud. It stops being obvious the moment it is written as numbers, because the big number in the picture ends up next to the small shape.
Before you read on. In your question there are 6 cubes and 5 cylinders, and the two towers are the same height.
Which shape is taller — one cube, or one cylinder?
Knowing which is taller is not enough. You need to know by how much — and for that, chop both towers into slices that are all the same size.
Slide until every dashed line lands on a join in both towers at once.
cube : cylinder = 5 : 6
Six cubes and five cylinders in the picture. Five and six in the working.
You do not have to draw thirty slices in an exam. Once you have seen why it works, the short version is just: swap the two numbers over. 6 cubes and 5 cylinders means the cube is 5 parts and the cylinder is 6.
From here on, nothing is new. One cylinder sitting on one cube is 803 cm — that is a total, and you have parts, so it is exactly An and Bình with different numbers.
On the last page the second check was optional politeness. Here it is the thing that saves you, and step 7 shows exactly how.
The tall figure was 803 cm.
365 + 438 = 803 ✓
6 cubes should equal 5 cylinders.
6 × 365 = 2190
5 × 438 = 2190 ✓
Suppose you had read the ratio straight off the picture — 6 cubes, 5 cylinders, so 6 : 5. Press it and see what happens.
Look at what the first check did there: it passed. Both versions add up to 803, because both use 11 parts. Adding back cannot tell them apart — it never could, and that is why one check is not enough.
The tower check can, because it is the only thing on the page that looks at the picture. When two answers both fit the number you were given, the one that also fits the drawing is the real one.
No score, no timer. A wrong pick tells you why and lets you try again.
8 coins stacked reach the same height as 5 blocks stacked. What is coin : block?
3 books stacked are as tall as 2 boxes. One book and one box together are 25 cm. How tall is the box?
Back to your question, but changed: this time you are told the cylinder is 73 cm taller than the cube, and nothing else. How tall is the cube?
Someone answers cube 438, cylinder 365. Which check spots the mistake?
1. Find the two towers that are the same height, and count the pieces in each. (Here: 6 and 5.)
2. Swap them. 6 cubes and 5 cylinders → cube is 5 parts, cylinder is 6. Write this line down and say why, in words.
3. From here it is a normal parts question: add the parts, one division, multiply back.
4. Check both ways — add them to the total, and multiply them back out into the two towers.
Step 2 is worth more than the rest put together, and it is the only step that is about looking rather than calculating. If a question has a picture in it, the picture is not decoration — it is one of the two numbers you need.