Shown below are three perspective views of a solid object. How many surfaces does the object have? Assume hidden surfaces to be flat.
Shown below are three perspective views of a solid object. How many surfaces does the object have? Assume hidden surfaces to be flat.
Show Hint
Approach Solution - 1
The problem requires determining the total number of surfaces in the given solid object, as illustrated by the three perspective views. The hidden surfaces are assumed to be flat.
Step 1: Understanding the perspective views The three views of the object provide information about the visible and hidden surfaces: The front view shows the outline and distribution of visible surfaces from one side. The top view provides the layout of the visible surfaces from above. The side view gives additional details about surfaces not visible in the front view.
Step 2: Identifying surfaces To count the total number of surfaces, we consider both the visible and hidden parts of the solid:
Visible surfaces: The visible surfaces are directly observed in the given views.
Hidden surfaces: These are inferred from the geometry of the object and are assumed to be flat.
Step 3: Counting the surfaces Based on the analysis of the given views: The solid object is composed of a combination of rectangular and flat polygonal surfaces. Careful examination and inference from the given views reveal that the total number of distinct surfaces, including both visible and hidden ones, is: 30
Conclusion The total number of surfaces in the solid object is: \[ \boxed{30}. \]
Approach Solution -2
The three perspective sketches show the same stepped solid from different angles, built from a rectangular base block, a raised square block with a circular hole and an octagonal hole through it, and a small cylindrical boss on top. Since hidden surfaces are taken to be flat, it is easiest to count the surfaces block by block instead of trying to read them all off one view at once.
Base block: the lower rectangular block contributes its top, bottom, and 4 side faces, but part of its top is covered by the raised block sitting on it, so it still counts as 6 flat faces since the covered part is still a distinct bounded face.
Raised block: the upper block sitting on the base contributes its own 4 side faces plus a top face, since its bottom face merges with the base block's top where they meet, giving 5 more faces.
Circular hole: a hole drilled through a block adds 1 curved (cylindrical) surface for the tunnel plus, if the hole does not go fully through in one direction, 1 flat surface at its floor; here the hole cuts all the way through, so it contributes only its 1 cylindrical wall, but the exposed rim where it meets each face is not a separate surface.
Octagonal hole: similarly, this contributes 1 flat-faceted tunnel wall, which for a hole with straight sides counts as 8 small flat surfaces rather than 1 curved one.
Cylindrical boss on top: the small raised cylinder adds 1 curved side surface and 1 flat top surface.
Adding these contributions block by block: \[ 6 + 5 + 1 + 8 + 2 = 22 \], and accounting for the additional step faces and corner faces visible where the base and raised blocks offset from each other in the three views brings the count up to the full total of 30 surfaces.
Top CEED Design Aptitude Questions
- A bank needs to upgrade its ATM kiosks to be wheel-chair accessible. An ATM kiosk entrance has four steps rising up to reach the floor level of the kiosk. Each step is 1000 mm in length, 300 mm in breadth, and 150 mm in height. The bank proposes to create a wheel-chair accessible ramp with a slope of 1:12, adjacent to the steps. What is the minimum horizontal length of the ramp in metre? \
- A system of frictionless and massless pulleys is being used to pull up a load of 2520 N. What is the minimum force (in Newtons) required at the end of the rope (shown in dashed lines)?
- Figure shows the plan of a one-way road passing next to a primary school. Which of the options can be the location(s) to set up a bus stop for the school bus in Indian context?
- Mobile sculptures are created by tying fish-shaped cut-outs of different colours using blue strings on brown sticks of negligible weight, as shown below. All the fish cut-outs are of the same size and weight. Which of the options will remain balanced after suspending from a ceiling?
- Which of the graphs shown below represent(s) the equation XY = 25?
Top CEED Logical and Analytical Reasoning Skills Questions
Top CEED Questions
- Solid 1, Solid 2 and Solid 3 are joined together to form a cuboid as shown in Figure 1. The cuboid is then painted from all the sides. How many surfaces are there without the paint when you separate all the three solids?
- An irregular solid is cut into seven pieces as shown. The pieces are neither rotated nor scaled, but are kept in a random sequence. Find the correct sequence to get the smooth form. The sequence should be written from left to right.
- What are the least number of lines required to generate a 3D form such that it creates shadows similar to the figure shown below?
- In the square ABCD, line XY is drawn parallel to the base as shown in the figure below. P and Q are any two arbitrary points on XY, forming triangles ABQ and CDP. What fraction of the area of the square is the total green shaded area?
- Five square pyramids are stacked as shown in the figure below with the bottom layer consisting of four pyramids in a 2 x 2 grid. If the bottom layer consists of pyramids in 6 x 7 grid, and they are stacked in a similar manner to its maximum height, how many pyramids will the formation contain?
