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#### Page No 16.10:

#### 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

#### Answer:

(a) 5 cm

$l=\sqrt{{r}^{2}+{h}^{2}}=\sqrt{{3}^{2}+{4}^{2}}=\sqrt{25}=5\mathrm{cm}$

#### Page No 16.10:

#### Question 8:

The number of faces of a triangular pyramid is

(a) 3

(b) 4

(c) 6

(d) 8

#### Answer:

(b) 4

( A pyramid is called a Triangular pyramid if its base is a triangle.)

#### Page No 16.10:

#### Question 9:

The number of edges of a triangular pyramid is

(a) 3

(b) 4

(c) 6

(d) 8

#### Answer:

(c) 6

#### Page No 16.10:

#### Question 10:

A tetrahedron is a pyramid whose base is a

(a) triangle

(b) square

(c) rectangle

(d) quadrilateral

#### Answer:

(a) Triangle

#### Page No 16.2:

#### Question 1:

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

(i) a cuboid

(ii) a cube

#### Answer:

(i) A lunch box, a compass box, a book and a duster.

(ii) A dice, a chalk box, a cubical cabin and a tissue box.

#### Page No 16.2:

#### Question 2:

Draw 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 edges.

#### Answer:

The diagram of a cuboid is shown below.

Faces -

PQRS (bottom)

TUVW (top)

TPQU(front)

WSRV (back)

TPSW (left)

UVRQ (right)

Edges -

PQ, QR, RS, SP

TU, UV, VW, WT

WS, SR, RV, VW

UV, VR, RQ, QU

#### Page No 16.2:

#### 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 name of its faces and edges.

#### Answer:

The cube is shown below:

A cube has 6 faces and 12 edges.

**Faces**

**Edges**

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

#### Page No 16.2:

#### 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.

#### Answer:

AE = DH = BF = CG = l

EF = AB = CD = GH = b

FG = EH = AD = BC = h

#### Page No 16.2:

#### Question 5:

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

#### Answer:

Following are the lateral faces for the base EFGH:

AEHD, AEFB, BFGC, DHGC

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

#### Page No 16.2:

#### Question 6:

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

Fgiure

#### Answer:

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

#### Page No 16.2:

#### Question 7:

In Fig. 16.2, name the

(i) face parallel to *BFGc*

(ii) faces adjacent ot *BFGC*

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

#### Answer:

(i) The face parallel to BFGC is AEHD.

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

(iii) GF, GH, CG

#### Page No 16.3:

#### 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 aline 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.

#### Answer:

(i) eight

(ii) twelve

(iii) six

(iv) four

(v) cube

(vi) edge

(vii) adjacent faces

(viii) three

(ix) cube

(x) vertex, or corner

#### Page No 16.3:

#### Question 9:

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

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

(ii) A cube has tweleve vertices

#### Answer:

(i) T

(ii) F

#### Page No 16.3:

#### 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.

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

#### Answer:

(i) UVWX is the base of the cuboid.

(ii) The lateral faces for the base UVWX are UXSP, QVWR, PQVU and SXWR.

(iii) Any one pair of opposite faces among the lateral faces of the base are PQVU and SXWR, or UXSP and QVWR.

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

The faces, which have VW as side, are QVWR and UVWX.

Faces which meet at vertex P are PQRS, UPSX and PQVU.

#### Page No 16.3:

#### Question 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 area equal to 20 cm^{2}?

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

(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?

#### Answer:

(i) The edges of 4 cm length are AD, EH, BC, and FG.

The edges of 5 cm length are AB, EF, CD and GH.

(ii) The faces having dimensions of 5 cm x 4 cm would have an area of 20 cm^{2}.^{ }And such faces are ABCD and EFGH.

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

(There are three pairs of opposite faces of equal area. The area of opposite faces are: 3 x 4 cm^{2}, 4 x 5 cm^{2}, and 3 x 5 cm^{2}.

And among these, 4 x 5 cm^{2}^{ }is the largest.

(iv) The faces having sides of 3 cm and 4 cm respectively would have the diagonal of 5 cm. (As hypotenuse of a right- angles triangle is: 3^{2} + 4^{2} = 5^{2}). Therefore, the faces ADHE and BCGF have the diagonal of 5 cm.

(v) The base has q dimension of 4 cm x 5 cm, so area of abase is: 4 x 5 = 20 cm^{2}.

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

#### Page No 16.9:

#### Question 1:

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

(i) Coen

(ii) Sphere

(iii) Cylinder

(iv) Cuboid

(v) Pyramid

#### Answer:

(i) A school bell and a funnel.

(ii) A tennis ball and a model of the globe.

(iii) Drink cans and delivering pipes for water and gas.

(iv) A match box and a brick.

(v) A paper-weight and a tower like the Eiffel Tower.

#### Page No 16.9:

#### 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.

#### Answer:

(i) My instrument box is in the shape of a cuboid.

(ii) A brick is in the shape of a cuboid.

(iii) A match box is in the shape of a cuboid.

(iv) A road-roller is in the shape of a cylinder.

#### Page No 16.9:

#### Question 1:

Total number of faces of a cuboid is

(a) 4

(b) 6

(c) 8

(d) 12

#### Answer:

(b) 6

#### Page No 16.9:

#### Question 2:

Total number of a cuboid is

(a) 4

(b) 6

(c) 8

(d) 12

#### Answer:

(d) 6

#### Page No 16.9:

#### Question 3:

Number of vertices of a cuboid is

(a) 4

(b) 6

(c) 8

(d) 10

#### Answer:

(c) 8

#### Page No 16.9:

#### 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

#### Answer:

(a) A dice

#### Page No 16.9:

#### Question 5:

A brick is an example of a

(a) cube

(b) cuboid

(c) prism

(d) cylinder

#### Answer:

(b) Cuboid

#### Page No 16.9:

#### Question 6:

A gas pipe is an example of a

(a) cone

(b) a cylinder

(c) cube

(d) sphere

#### Answer:

(b) A cylinder

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