Measures and solids · Ages 12–13

Three views worksheet

Part of: 3-D figures

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Measures and solids · Ages 12–13

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The solid is built of cubes, every column standing on the ground. How many squares do you see from the front?
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2.The solid is built of cubes, every column standing on the ground. How many squares do you see from above?
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3.The solid is built of cubes, every column standing on the ground. How many squares do you see from the right?
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4.The picture shows the three views of a solid built of cubes: the front view at the top left, the view from the right beside it (the front on its left), the view from above underneath (the back at the top). At most, how many cubes can it have?
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11.Count the cubes in the solid (every column on the ground): put the steps in order.
- A. With the back row = 11 + 3 + 3 + 1 = 18
- B. Front row = 2 + 2 + 1 = 5
- C. With the middle row = 5 + 3 + 2 + 1 = 11
Write the letters in the right order
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12.The picture shows the front view (top) and view from above (bottom, the back at the top) of a solid built of cubes. How far apart are the most and the fewest cubes it can have?
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13.A solid built of cubes: the picture shows its front view (top) and its view from above (bottom, the back at the top). It has at least cubes and at most .
Fill in each blank
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14.A warehouse piles cube crates as in the picture, every column on the floor. A photo taken from the right shows how many crate sides?
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15.All the cubes in the solid's front row are taken away. Then how many squares do you see from the right?
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16.Looking down on the solid, how many of the tops you see are on the 2nd layer or higher?
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Show the answers and working

Three views worksheet: Answers and working

1. 6 squares
Each column across shows only its tallest stack: 3 + 2 + 1 = 6; the shorter ones in front add nothing.
2. 7 squares
From above, each place with cubes shows one square however tall: 7 in all.
3. 15 squares
From the right, each row shows only its tallest column: front 5, middle 5, back 5; 5 + 5 + 5 = 15.
4. 9 cubes
The view from above shows where the cubes stand; each place can be at most the smaller of its column's tallest (front view) and its row's tallest (right view). Added up, at most 9.

5. A. A triangle
Stand right in front: a cube is a square, a cuboid or cylinder a rectangle, a cone, a pyramid or a triangular prism with its triangle to you a triangle, a sphere a circle.
6. B
From the front, each column across shows only its tallest stack: 3, 2 and 1 high, left to right.
7. A
From above, every place with cubes shows one square, whatever its height; the back row at the top, the front row at the bottom.
8. B
From the right, the front row is on the left and the back row on the right, each showing only its tallest column: 2, 2 and 3.
9. D
Take the two views together: a rectangle and a circle make a cylinder; a triangle and a circle with a dot, a cone; a triangle and a square with its diagonals, a square pyramid; a triangle and a rectangle with a middle line, a triangular prism; two circles, a sphere; two squares, a cube.
10. B
From above: a cube is a square, a cuboid a rectangle, a cylinder or sphere a circle, a cone a circle with a dot (its apex) in the middle, a lying triangular prism a rectangle with its top edge down the middle, a square pyramid a square with its slanting edges as diagonals.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

11. B → C → A
Row by row from the front: 5, then 11 with the middle row, then 18 with the back.
12. 3 cubes
Most: every place as tall as its column's tallest, 12; fewest: one place per column that tall and the rest 1 each, 9. 12 − 9 = 3.
13. 10, 13
Each column across: the top view gives its places, the front view its tallest. Fewest: one place that tall and the rest 1 each; most: every place that tall. 10 at least, 13 at most.
14. 10 sides
From the right each row shows only its tallest column: front 2, middle 3, back 5, 10 in all.
15. 4 squares
With the front row gone, the right view has the middle and back rows, each its tallest: 2 + 2 = 4.
16. 5 tops
From above each column shows its top cube only; columns 2 or more high have their tops on layer 2 or above: 5 of them.

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