RD Sharma Solutions Class 6 Maths Chapter 16 Understanding Three Dimensional Shapes

Exercise 16.1

Question 1: Name any four objects from your environment, which have the form of

(i)                  A cuboid

(ii)                A cube 

Solution 1:

(i)                  The objects which have the form of a cuboid from our environment are Bricks, Stacks of paper, laptop and refrigerator.

(ii)                 The objects which have the form of a cube from our environment are Dice, Rubik Cube, Ice Cube and toy Blocks.

Question 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 2:   The diagram of a cuboid is:

A cuboid has 6 faces and 12 edges.

According to the diagram the name of faces of a cube are PQRS, TUVW, WSRV, TPSW, UVRQ, and TPQU and the edges of a cube are PQ, QR, RS, SP, TU, UV, VW, WT, WS, SR, RV, VW and UV, VR, RQ, and QU.

Question 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 3:   The diagram of a cube is :

A cube has 6 faces and 12 edges.

According to the diagram the name of faces of a cube are ABCD, EFGH, ABFE, ADHE, BCGF, and CDHG and the edges of a cube are AB, BC, CD, DA, EF, FG, GH, HE, BF, CG, AE and HD

Question 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 4:   Given : the lengths of the edges AE = l, EF  = b and FG = h. The lengths of all other edges are as follows

AE = DH = BF = CG = l

EF = HG = AB = DC = b

FG = EH = BC = AD = h

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

Solution 5:

The lateral faces for the base EFGH are AEFB, AEHD, DHGC, and BFGC.

AE or BF or DH or CG  are the line segments representing the height of the cuboid are

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

Solution 6:

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

Question 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 7:

(i) ADHE is the face parallel to BFGC.

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

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

Question 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 the six faces are squares.

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

Solution 8:

(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 the six faces are squares.

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

Question 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 9:

Question 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

Solution 10:

(i) UVWX is the base of this cuboid.

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

(iii) PQVU and SRWX is the pair of opposite faces. There are two pairs of the opposite faces UXSP and QVWR and PQVU and SRWX among the lateral faces of the base.

(iv) The faces of this cuboid which have X as a vertex 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

Question 11:  The dimensions of a cuboid with vertices A, B, C, D, E, F, G and H are as shown

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

(ii) Which faces have area equal to 20cm²?

(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 11:

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

(ii)                 The faces have area equal to 20 cm² are ABCD and EFGH. The dimensions of 4 cm and 5 cm i.e. (4 × 5 = 20) have an area equal to 20 cm².

(iii)                Faces have the largest area are ABCD and EFGH. (4 × 5 = 20)20 cm² is the largest area.

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

(v)                 The area of the base of this cuboid is 20 cm²

(vi)               No, all the lateral faces have the different area. i.e., The two lateral faces have an area 3 × 5 = 15 cm² and the other have 3 × 4 = 12 cm² 

Exercise 12.2 

Question 1: Give two new examples of each of the following three dimensional shapes:

(i) Cone

(ii) Sphere

(iii) Cylinder

(iv) Cuboid

(v)  Pyramid 

Solution1 : 

Question 2: What is the shape of:

(i) your instrument box

(ii) a brick

(iii) a match box

(iv) a rod- roller

(v) a sweet laddoo 

Solution 2:

Objective Type Questions ::->

Mark the correct alternative in each of the following:

Question 1: Total number of faces of a cuboid is

(a) 4

(b) 6

(c) 8

(d) 12 

Solution 1:  The correct answer is (b).

Total number of faces of a cuboid is 6.

Question 2. Total number of edges of a cuboid is

(a) 4

(b) 6

(c) 8

(d) 12 

Solution 2: The correct answer is (d).

Total number of edges of a cuboid is 12.

Question 3. Number of vertices of a cuboid is

(a) 4

(b) 6

(c) 8

(d) 10 

Solution 3:  The correct answer is (c). 

Number of vertices of a cuboid is 8.

Question 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 4: The correct answer is (a). 

A Cuboid is an example of a dice.

Question 5.  A brick is an example of a

(a) Cube

(b) Cuboid

(c) Prism

(d) Cylinder 

Solution 5:   The correct answer is (b).

A cuboid is an example of brick .

Question 6:  A gas pipe is an example of a

(a) Cone

(b) A Cylinder

(c) Cube

(d) Sphere 

Solution 6:  The correct answer is (b).

A cylinder is an example of gas pipe.

Question 7: If the base radius and height of a right circular cone are 3 cm and 4 cm in lengths, then the slant height is

(a) 5 cm

(b) 2 cm

(c) 25 cm

(d) 6 cm 

Solution 7:  The correct answer is (a).

Slant height = √3² + 4² = √25 = 5 cm

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

Question 8: The number of faces of a triangular pyramid is

(a) 3

(b) 4

(c) 6

(d) 8 

Solution 8:  The correct answer is (b).

The number of 4 faces of a triangular pyramid.

Question 9: The number of edges of a triangular pyramid is

(a) 3

(b) 4

(c) 6

(d) 8 

Solution 9:  The correct answer is (c).

The number of 6 edges of a triangular pyramid.

Question 10: A tetrahedron is a pyramid whose base is a

(a) Triangle

(b) Square

(c) Rectangle

(d) Quadrilateral 

Solution 10:  The Correct answer is (a).

A tetrahedron is a pyramid whose base is a triangle.