Mathematics Worksheet: Shapes Around Us (Preparatory Stage)
Based on NCERT (demm101.pdf). Each question has a hidden answer and a detailed solution toggle for active learning!
Concepts
- What is a 3D shape? Give two examples.
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Answer: A shape with length, width, and height. Example: cube, cylinder.Show Solution
Solution: 3D shapes take up space—unlike 2D shapes (flat). Cubes (dice), cylinders (can) are common 3D shapes. - What do we call the flat surface of a 3D shape?
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Answer: FaceShow Solution
Solution: The “face” is any flat or curved surface that forms part of a solid. - Name a shape with no edges and no corners.
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Answer: SphereShow Solution
Solution: A sphere (like a ball) is perfectly round, no straight or pointy parts. - How many corners does a cube have?
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Answer: 8Show Solution
Solution: Where 3 faces meet is called a corner (vertex); a cube has eight. - If a box is unfolded flat, what is this shape called?
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Answer: NetShow Solution
Solution: “Net” is a flat pattern to fold into a box or other solid (demm101 activity, nets). - Which shape models a can? What faces does it have?
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Answer: Cylinder; two circles (bases) & one curved side.Show Solution
Solution: E.g., tin can: circular top/bottom, curved side wraps around. - What’s the difference between a prism and a pyramid?
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Answer: Prism has two equal ends, pyramid has one base and all faces meet at a point.Show Solution
Solution: Prisms: both ends same (cube, cuboid); pyramids: faces meet at the apex. - How are the faces, edges, and corners of a cube related?
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Answer: 6 faces, 12 edges, 8 corners; F + V – E = 2Show Solution
Solution: (Faces F) + (Vertices/corners V) – (Edges E) always equals 2 for 3D solids (Euler’s rule). - What shape is most rigid (doesn’t change when pushed)?
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Answer: TriangleShow Solution
Solution: Triangles don’t “collapse” unlike rectangles; tested using straws in book. - What do we call a straight line from the center of a circle to its edge?
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Answer: RadiusShow Solution
Solution: Important for drawing circles—radius is half of diameter.
Computational Skills
- How many faces does a cuboid have?
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Answer: 6Show Solution
Solution: Cuboids have 6 rectangular faces (like bricks and matchboxes). - How many vertices do a square pyramid and a triangular prism have?
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Answer: Square pyramid: 5; Triangular prism: 6Show Solution
Solution: Count corners in diagrams or real models, as in activity tables. - Draw a 3D shape with 2 circular faces and 1 curved face. What is it?
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Answer: CylinderShow Solution
Solution: E.g., tin can, drum. - How many sides does a pentagon have? How many angles?
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Answer: 5 sides, 5 anglesShow Solution
Solution: “Penta-” means five (star, house, etc.) - If a cube is colored on all six faces, then cut into 8 equal small cubes, how many will have 3 faces colored?
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Answer: 8 cubes (all corners)Show Solution
Solution: Every corner cube has three outside faces. - If a triangle is pushed gently, does its shape change? What about a rectangle?
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Answer: Triangle: No; Rectangle: YesShow Solution
Solution: Book’s activity: triangle is the most rigid shape. - How many right angles in a square?
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Answer: 4Show Solution
Solution: Each corner in a square is 90°; four in total. - Make a model using 8 cubes in a tower—how many cubes touch the table?
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Answer: 1Show Solution
Solution: In a vertical tower, only bottom cube touches the table. - If two lines meet at an angle greater than a right angle but less than a straight angle, what type is it?
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Answer: Obtuse angleShow Solution
Solution: 90° < angle < 180° - If a rectangle is made with 8 matchsticks, how many right angles are there?
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Answer: 4Show Solution
Solution: 4 corners = 4 right angles, always in rectangles.
Problem-Solving & Real World Modeling
- If you remove one piece from your model building (cube/brick), what can happen?
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Answer: Model structure could collapse or change shape.Show Solution
Solution: Removing a “support” weakens the model—models follow physical rules, just like real buildings. - Find three 3D shapes commonly used in real buildings.
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Answer: Cuboids (bricks), Cylinders (columns), Cones (minarets)Show Solution
Solution: India Gate pillars (rectangular prisms), Qutub Minar (cylinder/cone). - Name a shape with all faces the same: What real object is this?
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Answer: Cube; DiceShow Solution
Solution: Dice have six equal square faces (classic cube). - Why do builders favor rectangles for rooms and windows?
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Answer: Easier to construct and arrange; maximizes usable space.Show Solution
Solution: Rectangles tile with no gaps; fit together in straight lines. - If a circle is marked with 4 radii at equal distances, what shapes and angles do you see between them?
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Answer: 4 right angles (quarter circles)Show Solution
Solution: 360° ÷ 4 = 90° for each. - If you draw lines on a square to get two triangles, how many ways can you do this?
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Answer: 2 (diagonal each way)Show Solution
Solution: Each diagonal splits into two congruent triangles. - How many 2D flat faces can you see in a cuboid made from cardboard?
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Answer: 6Show Solution
Solution: Every cuboid (brick, box) has six rectangles/squares. - Create a "net" for a cube using paper: How many squares are in it?
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Answer: 6Show Solution
Solution: Cube always 6 faces (squares); various net patterns. - Challenge: Build a shape with 15 straws and 10 clay balls. What shape could you create? (Think pyramids/prisms.)
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Answer: Triangular prism or square pyramid (depends on triangle or square base)Show Solution
Solution: Use straws for edges, balls for corners/vertices as in chapter activity. - Challenge: How are a pentagon and a decagon similar? How are they different?
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Answer: Both are polygons; pentagon has 5 sides, decagon has 10.Show Solution
Solution: Both have equal sides/angles if regular, but differ in side/angle count.