Visualising Solid Shapes — Exercise 18.1

Draw an oblique sketch of a cube of side 3 units.

Answer

Steps of construction :

1. Take a squared paper of side 1 unit.

2. Draw a square of side 3 units to get the front face.

3. Draw the opposite face overlapping the first square. This square is 1 unit to the right and 1 unit above the previous square.

4. Join the corresponding corners of the two squares by oblique lines to get the required cube.

Draw an isometric sketch of a cube of side 3 units.

Answer

Steps of construction :

1. Take an isometric dot paper of side 1 unit.

2. Draw two base edges, each of length 3 units, along the two isometric directions from a common vertex.

3. Draw three vertical lines each of height 3 units, one on the middle vertex and the other two on the end points of these line segments.

4. For the top face, draw a rhombus of side 3 units whose adjacent sides are formed by joining the top free ends of the three vertical line segments to get the required cube.

Draw an oblique sketch of a cuboid of length 5 units, breadth 3 units and height 4 units.

Answer

Steps of construction :

1. Take a squared paper of side 1 unit.

2. Draw a rectangle of dimensions 5 units × 4 units to get the front face of the cuboid.

3. Draw the opposite face of the same size overlapping the first rectangle, such that it is 1 unit to the right and 1 unit above the first rectangle.

4. Join the corresponding corners of the two rectangles by oblique lines to get the required cuboid.

Draw an isometric sketch of a cuboid of length 5 units, breadth 3 units and height 4 units.

Answer

Steps of construction :

1. Take an isometric dot paper of side 1 unit.

2. From a common vertex, draw two base edges of lengths 5 units and 3 units along the two isometric directions.

3. Draw three vertical lines each of height 4 units, one on the middle vertex and the other two on the end points of these line segments.

4. For the top face, draw a parallelogram of length 5 units and breadth 3 units whose adjacent sides are formed by joining the top free ends of the three vertical line segments to get the required cuboid.

Draw an oblique sketch of a square pyramid of side 3 units and height 4 units.

Answer

Steps of construction :

1. Take a squared paper of side 1 unit.

2. Draw a square ABCD of side 3 units to get the base of the pyramid.

3. Draw the diagonals AC and BD of this square and let them meet at the point N.

4. Through N, draw a vertical line segment ON of length 4 units, where O is the vertex of the pyramid.

5. Join OA, OB, OC and OD to get the required square pyramid.

Draw an isometric sketch of a hexagonal prism of height 5 units and base a regular hexagon of side 2 units.

Answer

Steps of construction :

1. Take an isometric dot paper of side 1 unit.

2. Draw three consecutive sides of the base hexagon, each of length 2 units.

3. Draw four vertical lines each of height 5 units, one on each of the two middle vertices and the other two on the end points of these line segments.

4. Using the four upper endpoints as four vertices, complete a regular hexagon of side 2 units to obtain the upper face.