Exploring Some Geometric Themes

Class 8 · Mathematics Part 2 · 13 Questions

Draw the initial few steps (at least till Step 2) of the shape sequence that leads to the Sierpinski Triangle.

Find the number of holes, and the triangles that remain at each step of the shape sequence that leads to the Sierpinski Triangle.

3intermediate🔧 Apply5 marksNumerical

Find the area of the region remaining at the $n$ th step in each of the shape sequences that lead to the Sierpinski fractals. Take the area of the starting square/triangle to be 1 sq. unit.

1intermediate🔧 Apply3 marksDiagram

Draw the initial few steps (at least till Step 2) of the shape sequence that leads to the Koch Snowflake.

2intermediate🔧 Apply3 marksNumerical

Find the number of sides in the $n$ th step of the shape sequence that leads to the Koch Snowflake.

3intermediate🔧 Apply4 marksNumerical

Find the perimeter of the shape at the $n$ th step of the sequence. Take the starting equilateral triangle to have a sidelength of 1 unit.

3intermediate🔧 Apply4 marksDiagram

Draw a net of a cuboid having sidelengths: (i) 5 cm, 3 cm, and 1 cm (ii) 6 cm, 3 cm, and 2 cm

2intermediate🔧 Apply5 marksDiagram

Find the front view, top view and side view of each of the following solids, fixing its orientation with respect to the vertical, horizontal and side planes: cube, cuboid, parallelepiped, cylinder, cone, prism, and pyramid.

2advanced✨ Create5 marksShort Answer

Imagine eight identical cubes, glued together along faces to form the letter 'C'. (i) This looks like a 'C' from the front. What does it look like from the side? From the top? (ii) Glue additional cubes to make a shape that looks like 'C' from the front and 'P' from the top. (iii) Now, can you glue even more cubes to make it look like 'C' from the front, 'P' from the top, and 'P' from the side? (iv) Can you think of other letter combinations to make with a single combination of cubes in this manner?

6intermediate💡 Understand3 marksShort Answer

What are the different shapes the projection of a cube can make under different orientations?

1intermediate🔍 Analyze5 marksLong Answer

Show that by joining the midpoints of an equilateral triangle, we divide it into 4 identical equilateral triangles.

1intermediate🔧 Apply4 marksNumerical

If the congruent polygons of a prism have 10 sides, how many faces, edges and vertices does the prism have? What if the polygons have $n$ sides?

2intermediate🔧 Apply4 marksNumerical

If the base of a pyramid has 10 sides, how many faces, edges and vertices does the pyramid have? What if the base is an $n$ -sided polygon?