R d sharma mathematics solutions class 6 Solutions for Chapter 15 understanding three dimensional shapes

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

(i)a cuboid

(ii)a cube

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

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

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

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

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

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.

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.

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.

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 thisvertex.

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 area equal to 20 cm2?

(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?

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

(i)Cone

(ii)Sphere

(iii)Cylinder

(iv)Cuboid

(v)Pyramid

What is the shape of:

(i)your instrument box

(ii)a brick

(iii)a match box

(iv)a rod- roller

(v)a sweet laddoo

Total number of faces of a cuboid is

(a)4

(b)6

(c)8

(d)12

Total number of edges of a cuboid is

(a)4

(b)6

(c)8

(d)12

Number of vertices of a cuboid is

(a)4

(b)6

(c)8

(d)10

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 coneSolution

A brick is an example of a

(a)cube

(b)cuboid

(c)prism

(d)cylinder

A gas pipe is an example of a

(a)cone

(b)a cylinder

(c)cube

(d)sphere

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

The number of faces of a triangular pyramid is

(a)3

(b)4

(c)6

(d)8

The number of edges of a triangular pyramid is

(a)3

(b)4

(c)6

(d)8

A tetrahedron is a pyramid whose base is a

(a)triangle

(b)square

(c)rectangle

(d)quadrilateral