Exploring Some Geometric Themes Class 8 Very Short Question Answer

Exploring Some Geometric Themes Class 8 Very Short Question Answer

Exploring Some Geometric Themes Class 8 Very Short Question Answer

Question 1.

Find the number of holes at step 4 of creation of a Sierpinski carpet.

Solution:

The number of holes at step 4 = Sum of the first 4 terms of the sequence 1, 8, 64, ...

= 1 + 8 + 64 + 512 = 585.

Question 2.

Find the number of remaining triangles at the step 5 in creating the shape of Sierpinski triangles.

Solution:

At step 5, the number of remaining triangles is the 5th term of the sequence 1, 3, 9, 27, ... = 3^5-1 = 3⁴ = 81.

Question 3.

Find the number of faces of a solid shape (having polygonal faces) of edges 24 and vertices 16.

Solution:

Using Euler’s formula,

F + V - E = 2

We have F + 16 - 24 = 2

⇒ F = 2 + 24 - 16 = 10.

Question 4.

What will be the length of a projected line segment when the projected line segment of length 8 cm is parallel to the plane of projection ?

Solution:

When the projected line segment is parallel to the plane of projection, then its length is equal to actual length of the line segment.

So, required length = 8 cm.

Question 5.

What can be the projections of a parallelogram under different orientations.

Solution:

The required projections can be a parallelogram, rhombus, square, kite, rect¬angle, trapezium and even a line segment.