Geometrical Constructions (Copy)
Q1 (Non-Calculator)
Draw a straight line 7 cm long.
Solution:
- Place the ruler on the paper.
- Mark two points exactly 7 cm apart.
- Draw a straight line joining the two points.
Answer:
Straight line of 7 cm accurately drawn.
Q2 (Non-Calculator)
Using a ruler and protractor, draw an angle of 60° starting from a given point.
Solution:
- Draw a base line with a ruler.
- Place the centre of the protractor on the starting point.
- Mark a point at 60° using the protractor scale.
- Join the starting point to the 60° mark with a ruler.
Answer:
An angle of 60° correctly drawn.
Q3 (Non-Calculator)
Construct a triangle with sides 5 cm, 6 cm, and 7 cm using ruler and compasses only. Show construction arcs.
Solution:
- Draw the base of 5 cm using a ruler.
- Set compass to 6 cm, draw an arc from one end of the base.
- Set compass to 7 cm, draw an arc from the other end of the base.
- Mark the intersection point of the arcs.
- Join this point to both ends of the base with a ruler.
Answer:
Triangle with sides 5 cm, 6 cm, and 7 cm correctly constructed with visible arcs.
Q4 (Non-Calculator)
Name a solid whose net consists of 6 equal squares.
Solution:
A cube.
Answer:
Cube
Q5 (Non-Calculator)
Draw a simple net of a cuboid with length 5 cm, width 3 cm, and height 2 cm.
Solution:
- Draw two rectangles of 5 cm by 3 cm (top and bottom).
- Draw two rectangles of 5 cm by 2 cm (front and back).
- Draw two rectangles of 3 cm by 2 cm (sides).
- Arrange them in a cross-like shape with matching sides joined.
Answer:
Correct net of cuboid with labeled dimensions.
Q6 (Calculator)
The net of a cube is given. Each square has a side length of 4 cm. Find the surface area of the cube.
Solution:
- Area of one square = 4 × 4 = 16 cm²
- Surface area = 6 × 16 = 96 cm²
Answer:
96 cm²
Q7 (Calculator)
A net of a cuboid shows dimensions: length 10 cm, width 5 cm, height 3 cm. Find the volume.
Solution:
Volume = length × width × height
Volume = 10 × 5 × 3 = 150 cm³
Answer:
150 cm³
Q8 (Calculator)
The net of a triangular prism is given. Base area of triangle = 12 cm², length = 8 cm. Find the volume.
Solution:
Volume = area of cross-section × length
Volume = 12 × 8 = 96 cm³
Answer:
96 cm³
Q9 (Calculator)
A solid is made by joining two cubes of side 3 cm together. Find the total surface area.
Solution:
- Surface area of one cube = 6 × (3 × 3) = 54 cm²
- When joined, 1 face from each cube is hidden.
- Total surface area = (2 × 54) – (2 × 9) = 108 – 18 = 90 cm²
Answer:
90 cm²
Q10 (Calculator)
Draw the net of a square-based pyramid.
Solution:
- Draw a square for the base.
- Draw 4 equal triangles (isosceles) attached to each side of the square.
Answer:
Correct net of a square-based pyramid with one square and four attached triangles.