Question 15
Which solid corresponds to the given top view, front view, and side view?
Solids to choose from:
We need to find the 3D solid that matches the given Front View, Top View, and Side View.
Step 1 — Analyze the given 2D views
Let us carefully examine the three given 2D views. We will assume a standard orientation: Front View from the front (X-Z plane), Top View from the top (X-Y plane), and Side View from the right (Y-Z plane).
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Front View:
- This view shows a vertical column of 3 blocks on the left side (at x=0).
- It also shows a horizontal arm of 2 blocks extending to the right from the middle block of the vertical column (at x=1 and x=2, at z=1).
- The total width of this view is 3 units.
- The total height is 3 units.
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Top View:
- This view shows a horizontal row of 3 blocks at the back (at y=0, across x=0, x=1, x=2).
- It also shows a vertical column of 2 blocks extending forward (at y=1, at x=0).
- The total width of this view is 3 units.
- The total depth is 2 units.
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Side View:
- This view shows a vertical column of 3 blocks at the front (at y=0, across z=0, z=1, z=2).
- It also shows a single block at the back (at y=1) at the top level (z=2).
- And another single block at the back (at y=1) at the bottom level (z=0).
- The middle block at the back (y=1, z=1) is missing.
- The total depth of this view is 2 units.
- The total height is 3 units.
Step 2 — Evaluate each solid (i) to (vii)
We will now examine each solid from (i) to (vii) and determine its Front, Top, and Side views based on the arrows provided on each solid. Then we will compare these derived views with the given views.
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Solid (i):
- Front View: Matches the given Front View (3 blocks wide, arm at middle height).
- Top View: Matches the given Top View (3 blocks at back, 1 block at front-left).
- Side View: Shows a complete 2x3 rectangle (a 3-block high column at y=0 and another 3-block high column at y=1). This does NOT match the given Side View, which has a gap in the middle.
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Solid (ii):
- Front View: The horizontal arm extends from the bottom block of the vertical column. This does NOT match the given Front View (arm is at middle height).
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Solid (iii):
- Front View: Matches the given Front View.
- Top View: Shows a single block at the front-left (y=0, x=0) and a 3-block wide row at the back (y=1, across x=0, x=1, x=2). This does NOT match the given Top View.
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Solid (iv):
- Front View: The horizontal arm extends from the top block of the vertical column. This does NOT match the given Front View (arm is at middle height).
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Solid (v):
- Front View: Matches the given Front View.
- Top View: Matches the given Top View.
- Side View: Shows a 3-block high column at the front (y=0). At the back (y=1), it shows a block at the bottom (z=0) and a block at the top (z=2), with the middle block (z=1) missing. This matches the given Side View.
- Since all three views match, Solid (v) is the correct answer.
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Solid (vi):
- Front View: Matches the given Front View.
- Top View: Shows a single block at the front-left (y=0, x=0) and a 3-block wide row at the back (y=1, across x=0, x=1, x=2). This does NOT match the given Top View.
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Solid (vii):
- Front View: Matches the given Front View.
- Top View: Shows a single block at the front-left (y=0, x=0) and a 3-block wide row at the back (y=1, across x=0, x=1, x=2). This does NOT match the given Top View.
Therefore, Solid (v) is the only one that corresponds to all three given views.
Answer
(v)
More questions in FIO
Draw the initial few steps (at least till Step 2) of the shape sequence that leads to the Sierpinski Triangle.
Find the number of holes, and the triangles that remain at each step of the shape sequence that leads to the Sierpinski Triangle.
Find the area of the region remaining at the th step in each of the shape sequences that lead to the Sierpinski fractals. Take the area of the starting square/triangle to be 1 sq. unit.
Draw the initial few steps (at least till Step 2) of the shape sequence that leads to the Koch Snowflake.
Find the number of sides in the nth step of the shape sequence that leads to the Koch Snowflake.
Find the perimeter of the shape at the nth step of the sequence. Take the starting equilateral triangle to have a sidelength of 1 unit.
Figure it Out
- Which of the following are the nets of a cube? First, try to answer by visualisation. Then, you may use cutouts and try.
A cube has 11 possible net structures in total. In this count, two nets are considered the same if one can be obtained from the other by a rotation or a flip. For example, the following nets are all considered the same —
Find all the 11 nets of a cube.
Draw a net of a cuboid having sidelengths:
(i) 5 cm, 3 cm, and 1 cm
(ii) 6 cm, 3 cm, and 2 cm
Observe the front view, top view and side view of the different lines in Fig. 4.6. Is there any relation between their lengths?
Find the front view, top view and side view of each of the following solids, fixing its orientation with respect to the vertical, horizontal and side planes: cube, cuboid, parallelepiped, cylinder, cone, prism, and pyramid. If needed, see the next problem for clues.
Match each of the following objects with its projections.
Draw the top view, front view and the side view of each of the following combinations of identical cubes.
Imagine eight identical cubes, glued together along faces to form the letter 'C'.
Which solid corresponds to the given top view, front view, and side view?
Solids to choose from:
Using identical cubes, make a solid that gives the following projections:
Find the number of cubes in this stack of identical cubes.
What are the different shapes the projection of a cube can make under different orientations?
In addition to the 5 ways shown in Fig. 4.8, are there any additional ways of gluing four cubes together along faces? Can you visualise and draw these as well?
Draw the following figures on the isometric grid.
[Hint: It may be useful to determine whether the edge to be currently drawn — say, along the height — goes from down to up or up to down. Accordingly, draw the line segment on the grid either in the direction of the height axis or opposite to it.]
Is there anything strange about the path of this ball? Recreate it on the isometric grid.
[Hint: Consider a portion of this figure that is physically realisable and identify the 3 primary directions.]
Observe this triangle.
(i) Would it be possible to build a model out of actual cubes? What are the front, top, and side profiles of this impossible triangle? (ii) Recreate this on an isometric grid. (iii) Why does the illusion work?