RD Sharma Solutions Class 6 Mathematics Solutions for Exercise 16.1 in Chapter 15 - Understanding Three Dimensional Shapes

Question 10 Exercise 16.1

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.

Answer:

(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.

We know that 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.

We know that the faces which meet at this vertex P are PQRS, UPSX and PQVU

Video transcript

"hello student welcome back to the lead without solving session and in today's session we are going to discuss one more question related to geometry all right so first i am going to read the statement of the question on a common hypotenuse a b okay this is the common hypotenuse db two right triangles okay a c b and a d b are situated on the opposite sides and we are going to prove that angle b a z this is angle b a c is equals to angle b d c angle b d c all right so let's solve this question so according to the given question okay uh two right triangles are given here all right okay that means okay triangle a c b and triangle abd a b b okay are the two two right triangle right triangle okay which is having the same hypotenuse right same hypotenuse a b all right okay and here we are going to prove okay we are going to prove so we are going to prove that angle at the angle at a that means angle bac is equals to angle bd c all right so as we know that okay um triangle a c b and a d b are the right triangle here right and which is having the same hypotenuse okay that means okay angle at c that is angle c is equals to angle d okay which is 90 degree all right okay and that means angle at c plus angle at t is equals to 90 degree plus 90 degree that is 180 degree right okay and that's why quadrilateral the given quadrilateral a b c d is a cyclic quadricep quadrilateral it is a cyclic quadrilateral quadrilateral okay as all the vertices are lying on the circle and okay the sum of sum of opposite angles is equals to 180 degree all right okay that means the given quadrilateral abcd or it is abb c okay is a cyclic correlator all right so okay and again if you carefully observe that okay angle bac angle b a c and angle bdc angle okay so both the angles lie in a same segment right in a same segment okay that is segment bc all right okay both the angles are lying on a in a same segment that is or in a segment bc okay and okay when the angles lie on the same on the same segment the angles are equal right and that's why okay we can say that angle be a c is equals to angle b d c because okay both the angles lie in same segment same segment all right okay that means okay angle bac is equals to angle bdc has proven right okay so that's why the statement has fruits so it is henceforth all right so that is all about today's session um if you are any doubt please leave your comment below and please subscribe to this channel thanks for watching the video bye "

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Exercises

Exercise 16.1

Exercise 16.2

Chapters

Knowing your numbers