Question Video: Matching a Shape to Given Plan, Front, and Side Views Mathematics • 7th Grade

Which of the following is the solid shape that could have the views shown? [A] Option (A) [B] Option (B) [C] Option (C) [D] Option (D) [E] Option (E)

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Video Transcript

Which of the following is the solid shape that could have the views shown?

In this question, we’re given three different views in two dimensions of a three-dimensional shape. We’re then given five different three-dimensional shapes, and we need to work out which one of these has the elevations and plan given. Let’s begin by recalling that an elevation is a two-dimensional drawing of a three-dimensional shape from either the side or the front. The side elevation is from the side, and the front elevation is from the front. Like an elevation, a plan is also a two-dimensional drawing, but this time it’s when viewed from above the shape.

So let’s begin by looking at the side elevation. We can see that there’s three squares on the base and one square above. Let’s have a look at each of the three-dimensional shapes given in the options, and we need to be careful that we’re looking at the shape from the correct given side. We can shade the parts of the three-dimensional shape that we would see from the side. If we look at option (A), it is in fact incorrect. The side elevation of option (A) would look like this. That’d be three squares on the top and one square underneath on the left-hand side. We can eliminate option (A) because the side elevation is incorrect. If we look at option (B) from the side, we have the three squares on the base and this one square on top. Therefore, at least the side elevation of option (B) would be correct.

Let’s see if any of the other shapes would have the same side elevation. In option (C), there’d be side elevation with one square at the base and three squares along the top. It would in fact have the same side elevation as that in option (A). It is, however, incorrect as it wouldn’t fit the given side elevation. Option (D) would have two squares on the base and three squares along the top, which wouldn’t fit the side elevation. If we shade in what we would see in option (E), we can see that this would also be incorrect. It looks like we have eliminated all of the options except for option (B). So let’s check if the front elevation is also correct.

What we’re looking for in the front elevation is identical to that in the side elevation, three squares on the base and one square on the top on the left side. If we look at option (B), we’ve got three squares on the base and one square sitting on top on the left side. So the front elevation here is also correct. For the plan view then, that’s the two-dimensional shape that we would see if we looked downwards from above. Shading in the parts of the blocks that we would see from above, we can see that the plan view given would also fit with shape (B). We can therefore give our answer that the shape given in option (B) would have the views of the side elevation, front elevation, and plan that we were given.