RS Aggarwal Class 7 Mathematics Solutions Chapter 19 Three-Dimensional Shapes

Question 1. (i) A cuboid has 6 rectangular faces, 12 edges and 8 vertices.
Answer: A cuboid is a solid shape with 6 rectangular surfaces. It has 12 straight edges where faces meet, and 8 corner points where edges connect.
In simple words: Think of a box - it has 6 flat sides, 12 lines along the edges, and 8 corners.

Exam Tip: Memorise these three properties as they are the defining features of a cuboid and help distinguish it from other 3D shapes.

Question 1. (ii) A cylinder has 1 curved face and 2 flat faces.
Answer: A cylinder is a solid with a curved surface and two circular flat bases - one on top and one on the bottom. The curved surface wraps around between these two circles.
In simple words: Picture a tin can - the side is curved and the top and bottom are flat circles.

Exam Tip: A cylinder has no edges (the curves are smooth), unlike a cuboid which has sharp edges where faces meet.

Question 1. (iii) A cone has one curved face and one flat face.
Answer: A cone has a single curved surface and one flat circular base. The curved part comes to a point at the top, called the apex, above the circular base.
In simple words: Imagine an ice cream cone - the pointy part is where the curved surface meets the circular opening at the bottom.

Exam Tip: Notice that a cone tapers to a single point, which is what makes it different from a cylinder that stays the same width throughout.

Question 1. (iv) A sphere has a curved surface.
Answer: A sphere is a perfectly round solid shape with only one curved surface and no flat faces or edges. Every point on its surface is the same distance from its centre.
In simple words: A ball or a globe is a sphere - it is round in all directions.

Exam Tip: A sphere is the only 3D shape with zero flat faces and zero edges - it is completely curved.

Question 2. (i) True
Answer: This statement is correct. A cuboid does indeed have 6 rectangular faces arranged in three pairs of opposite faces.
In simple words: A cuboid (like a shoebox) has 6 sides, and opposite sides match each other.

Exam Tip: Always verify such statements by visualising the shape or counting the faces mentally before confirming true or false.

Question 2. (ii) True
Answer: This statement is accurate. A cylinder does have 1 curved face (the side) and 2 flat faces (the two circular bases at top and bottom).
In simple words: When you look at a cylinder from the side, you see a curve. When you look at the top or bottom, you see a flat circle.

Exam Tip: Count the different types of surfaces separately - curved surfaces and flat surfaces - to avoid confusion.

Question 2. (iii) True
Answer: This statement is true. A cone does have one curved face and one flat face - the curved side surface and the flat circular base.
In simple words: A cone has a pointy curved side and a flat circular bottom.

Exam Tip: Do not confuse the apex (point) with an edge - the point is part of the curved surface, not a separate feature.

Question 2. (iv) False
Answer: This statement is incorrect. A sphere does not have a flat face - it has only a single curved surface. All points on a sphere are curved, with no flat portions anywhere.
In simple words: A ball is curved everywhere - there are no flat spots on it at all.

Exam Tip: The key word here is "only" - if a shape has any flat face, it cannot be purely curved.

Question 2. (v) True
Answer: This statement is correct. A cube is indeed a special type of cuboid where all 6 faces are squares of equal size (instead of rectangles).
In simple words: A cube is just a cuboid where every side is a square instead of a rectangle.

Exam Tip: All cubes are cuboids, but not all cuboids are cubes - this relationship is important to remember.

Question 3. (i) Conical Flask, Funnel, Ice Cream, Birthday Cap, Top
Answer: These are all examples of cone-shaped objects. A conical flask is laboratory equipment with a pointed bottom, a funnel narrows from wide to narrow to pour liquids, an ice cream cone holds the frozen treat, a birthday cap comes to a point, and a top (spinning toy) has a conical shape that tapers to a point.
In simple words: All of these things have a point at the top or bottom and a round opening or base.

Exam Tip: When identifying cone-shaped objects, look for that characteristic point (apex) and the circular base - these are the defining features of a cone.

Question 3. (ii) Cricket Ball, Foot Ball, Orange, Earth, Sun
Answer: These are all spherical (sphere-shaped) objects. A cricket ball and football are sports equipment that are round in all directions, an orange is a round fruit, the Earth is a sphere rotating on its axis, and the Sun is a massive sphere of hot gas in space. Each of these objects is perfectly round from every angle.
In simple words: All of these things are ball-shaped or round - they look the same no matter which way you turn them.

Exam Tip: Sphere-shaped objects do not have any flat parts or pointed parts - they are round in all directions.

Question 3. (iii) Brick, Book, Eraser, Chocolate Bar, Mobile Phone
Answer: These are all cuboid (rectangular box-shaped) objects. A brick is a building block with flat rectangular faces, a book is a rectangular box shape, an eraser is typically cuboid, a chocolate bar has flat rectangular sides, and a mobile phone is a rectangular solid with flat surfaces. All of these items have 6 rectangular (or nearly rectangular) faces, 12 edges, and 8 vertices.
In simple words: All of these things are shaped like a box with flat sides and sharp corners.

Exam Tip: When identifying cuboid objects, count or visualise the flat faces - if you see 6 flat surfaces arranged in a box pattern, it is a cuboid.

Question 3. (iv) Circular Pipe, Gas Cylinder, Round Water Bottle, Mercury Tube, Pen
Answer: These are all cylindrical (cylinder-shaped) objects. A circular pipe is hollow and circular in cross-section, a gas cylinder is a tall metal container with curved sides, a round water bottle has a cylindrical body, a mercury tube is a glass cylinder, and a pen barrel is cylindrical in shape. Each of these objects has two circular bases and a curved side surface connecting them.
In simple words: All of these items are tube-shaped or can-shaped - round and straight, with circular openings at the ends.

Exam Tip: Cylindrical objects have curved sides that wrap around evenly, and you can see circular openings at both ends (or at least imagine them).