Chapter 16 consists of topics which help students understand Three-Dimensional Shapes, which we generally see in our daily lives. Each of these shapes is a solid and not a flat shape. We will also learn other important terms like faces, edges and vertices, etc., which are associated with these shapes. Here, we get to know about shapes like cuboids, cubes, cylinders, right circular cones, spheres, pyramids and tetrahedrons.

These concepts are explained in an interactive manner by subject-matter experts based on the latest CBSE guidelines. To build a better knowledge of the concepts which are explained in this chapter, students can make use of RD Sharma Solutions for Class 6 **Chapter 16 Understanding Three-Dimensional Shapes** PDF, which is provided here.

### RD Sharma Solutions for Class 6 Maths Chapter 16: Understanding Three-Dimensional Shapes Download the PDF

## Access answers to Maths RD Sharma Solutions for Class 6 Chapter 16: Understanding Three-Dimensional Shapes

### Exercise 16.1 page: 16.2

**1. Name any four objects from your environment which have the form of **

**(i) a cuboid (ii) a cube**

**Solution:**

(i) The objects which have the form of a cuboid are a compass box, a lunch box, a duster and a book.

(ii) The objects which have the form of a cube are a chalk box, a disc, a tissue box and a cubical cabin.

**2. Draw a diagram to represent a cuboid. Label its vertices as P, Q, R, S, T, U, V and W. Now write the names of its faces and its edges.**

**Solution:**

The diagram of a cuboid is given below

The faces of a cuboid are

The bottom face – PQRS

The top face – TUVW

The back face – WSRV

The left face – TPSW

The right face – UVRQ

The front face – TPQU

The edges of a cuboid are

(PQ, QR, RS, SP), (TU, UV, VW, WT), (WS, SR, RV, VW) and (UV, VR, RQ, QU)

**3. Draw a diagram to represent a cube. Label its vertices as A, B, C, D, E, F, G and H. Now write the names of its faces and edges.**

**Solution:**

The diagram of a cube is as follows:

We know that a cube has 6 faces and 12 edges.

The faces of a cube are

ABCD, EFGH, BCGF, ADHE, ABFE and CDHG.

The edges of a cube are

AB, BC, CD, DA, EF, FG, GH, HE, BF, CG, AE and HD

**4. Fig. 16.2 represents a cuboid. The lengths of the edges AE, EF, and FG are indicated as l, b and h, respectively. Indicated the lengths of all other edges.**

**Solution:**

It is given that the lengths of the edges AE, EF and FG are indicated as l, b and h, respectively. The lengths of all other edges are as follows

AE = DH = BF = CG = l

EF = HG = AB = DC = b

FG = EH = BC = AD = h

**5. In Fig. 16.2, if the face EFGH is taken as the base, the name of the lateral faces. Also, name the line segment representing the height of the cuboid.**

**Solution:**

The lateral faces for the base EFGH are

AEHD, AEFB, BFGC and DHGC

The line segments representing the height of the cuboid are

AE or DH or BF or CG

**6. In Fig. 16.2, name the four diagonals of the cuboid.**

**Solution:**

CE, BH, AG and DF are the four diagonals of a cuboid.

**7. In Fig. 16.2, name the**

**(i) face parallel to BFGC**

**(ii) faces adjacent to BFGC**

**(iii) three edges which meet in the vertex G.**

**Solution:**

(i) AEHD is the face parallel to BFGC.

(ii) BCDA, DCGH, ABFE, and EFGH are the faces adjacent to BFGC.

(iii) Three edges which meet in the vertex G are CG, GH and GF.

**8. Fill in the blanks to make the following statements true:**

**(i) A cuboid has …… vertices.**

**(ii) A cuboid has …… edges**

**(iii) A cuboid has ……. Faces.**

**(iv) The number of lateral faces of a cuboid is ……..**

**(v) A cuboid, all of whose edges are equal, is called a …….**

**(vi) Two adjacent faces of a cuboid meet in a line segment called its …….**

**(vii) Each edge of a cuboid can be obtained as a line segment in which two …… meet.**

**(viii) ……edges of a cube (or cuboid) meet at each of its vertices.**

**(ix) A ……. is a cuboid in which all six faces are squares.**

**(x) The three concurrent edges of a cuboid meet at a point called the …… of the cuboid.**

**Solution:**

(i) A cuboid has eight vertices.

(ii) A cuboid has twelve edges.

(iii) A cuboid has six faces.

(iv) The number of lateral faces of a cuboid is four.

(v) A cuboid, all of whose edges are equal, is called a cube.

(vi) Two adjacent faces of a cuboid meet in a line segment called its edge.

(vii) Each edge of a cuboid can be obtained as a line segment in which two adjacent faces meet.

(viii) Three edges of a cube (or cuboid) meet at each of its vertices.

(ix) A cube is a cuboid in which all six faces are squares.

(x) The three concurrent edges of a cuboid meet at a point called the vertex of the cuboid.

**9. In each of the following, state if the statement is true (T) or false (F):**

**(i) Number of faces in a cuboid and the number of faces in a cube are equal.**

**(ii) A cube has twelve vertices.**

**Solution:**

(i) True

(ii) False

**10. For the cuboid shown in Fig. 16.3,**

**(i) What is the base of this cuboid?**

**(ii) What are the lateral faces of this cuboid?**

**(iii) Name one pair of opposite faces. How many pairs of opposite faces are there? Name them.**

**(iv) Name all the faces of this cuboid which have X as a vertex. Also, name those which have VW as a side **

**(v) Name the edges of this cuboid which meet at the vertex P. Also, name those faces which meet at this vertex.**

**Solution:**

(i) The base of this cuboid is UVWX.

(ii) The lateral faces of this cuboid are UXSP, QVWR, SXWR and UVQP.

(iii) One pair of opposite faces among the lateral faces of the base are PQVU and SXWR or UXSP and QVWR. We know that a cuboid has two pairs of opposite faces among the lateral faces of the base.

(iv) The faces of this cuboid which have vertex as X, are UVWX, UXSP and SXWR.

The faces having VW as a side are UVWX and QVWR.

(v) The edges of this cuboid meeting at the vertex P are UP, PQ and PS.

The faces which meet at this vertex P are PQRS, UPSX and PQVU.

**11. The dimensions of a cuboid with vertices A, B, C, D, E, F, G and H are as shown in Fig. 16.4.**

**(i) Which edges are of length 4 cm? Which edges are of length 5 cm?**

**(ii) Which faces have an area equal to 20 cm ^{2}?**

**(iii) Which faces have the largest area? What is this largest area?**

**(iv) Which faces have a diagonal equal to 5 cm?**

**(v) What is the area of the base of this cuboid?**

**(vi) Do all the lateral faces have the same area?**

**Solution:**

(i) The edges of length 4 cm are BC, EH and FG, and the edges of length 5 cm are DC, EF and HG.

(ii) The faces which have the dimensions of 4 cm and 5 cm, i.e., (4 × 5 = 20), have an area equal to 20 cm^{2}. ABCD and EFGH have an area equal to 20 cm^{2}

(iii) ABCD and EFGH have the largest area. 20 cm^{2} is the largest area.

(iv) The faces having sides 4 cm and 3 cm would have a diagonal of 5 cm, and the faces are ADHE and BCGF.

(v) The area of the base of this cuboid is 20 cm^{2}

(vi) No, all the lateral faces do not have the same area. The two lateral faces have an area 3 × 5 = 15 cm^{2} and the other have 3 × 4 = 12 cm^{2}

### Exercise 16.2 PAGE: 16.9

**1. Give two new examples of each of the following three-dimensional shapes:**

**(i) Cone**

**(ii) Sphere**

**(iii) Cylinder**

**(iv) Cuboid**

**(v) Pyramid**

**Solution:**

(i) The examples of a cone are a funnel and a school bell.

(ii) The examples of a sphere are a tennis ball and a model of a globe.

(iii) Examples of a cylinder are drink cans and delivering pipes for water and gas.

(iv) Examples of cuboids are a matchbox and brick.

(v) The examples of pyramids are paperweight and a tower like the Eiffel Tower.

**2. What is the shape of:**

**(i) your instrument box**

**(ii) a brick**

**(iii) a matchbox**

**(iv) a rod-roller**

**(v) a sweet laddoo**

**Solutions:**

(i) Your instrument box – cuboid shape

(ii) A brick – Cuboid shape

(iii) A match box – Cuboid shape

(iv) A road-roller – Cylinder shape

(v) A sweet laddoo – Sphere shape

### Objective Type Questions page: 16.9

**Mark the correct alternative in each of the following:**

**1. Total number of faces of a cuboid is **

**(a) 4 (b) 6 (c) 8 (d) 12**

**Solution:**

Option (b) is the correct answer.

The total number of faces of a cuboid is 6.

**2. Total number of edges of a cuboid is **

**(a) 4 (b) 6 (c) 8 (d) 12**

**Solution:**

Option (d) is the correct answer.

The total number of edges of a cuboid is 12.

**3. Number of vertices of a cuboid is**

**(a) 4 (b) 6 (c) 8 (d) 10**

**Solution:**

Option (c) is the correct answer.

The number of vertices of a cuboid is 8.

**4. Which one of the following is an example of a cuboid?**

**(a) a dice (b) a football (c) a gas pipe (d) an ice-cream cone**

**Solution:**

Option (a) is the correct answer.

An example of a cuboid is a dice.

**5. A brick is an example of a **

**(a) cube (b) cuboid (c) prism (d) cylinder**

**Solution:**

Option (b) is the correct answer.

Brick is an example of a cuboid.

**6. A gas pipe is an example of a**

**(a) cone (b) a cylinder (c) cube (d) sphere**

**Solution:**

Option (b) is the correct answer.

A gas pipe is an example of a cylinder.

**7. If the base radius and height of a right circular cone are 3 cm and 4 cm in length, then the slant height is**

**(a) 5 cm (b) 2 cm (c) 25 cm (d) 6 cm**

**Solution:**

Option (a) is the correct answer.

If the base radius and height of a right circular cone are 3 cm and 4 cm in length, then the slant height is 5 cm.

Slant height = √3^{2} + 4^{2} = √25 = 5 cm

**8. The number of faces of a triangular pyramid is**

**(a) 3 (b) 4 (c) 6 (d) 8**

**Solution:**

Option (b) is the correct answer.

The number of faces of a triangular pyramid is 4.

**9. The number of edges of a triangular pyramid is**

**(a) 3 (b) 4 (c) 6 (d) 8**

**Solution:**

Option (c) is the correct answer.

The number of edges of a triangular pyramid is 6.

**10. A tetrahedron is a pyramid whose base is a**

**(a) triangle (b) square (c) rectangle (d) quadrilateral**

**Solution:**

Option (a) is the correct answer.

A tetrahedron is a pyramid whose base is a triangle.

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