GSEB Class 7 Maths Solutions Chapter 15 Visualising Solid Shapes Exercise 15.4

Question 1. A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then then answer these questions).
(i) A ball
(ii) A cylindrical pipe
(iii) A book
Answer:
When light shines directly above a solid object:
(i) For a ball, the shadow appears circular.
(ii) For a cylindrical pipe, the shadow looks like a rectangle.
(iii) For a book, the shadow will mostly resemble a rectangle.
In simple words: When light is above, a ball makes a round shadow, a pipe makes a long, flat shadow, and a book also makes a long, flat shadow.

Exam Tip: Understand how different 3-D shapes cast shadows based on the light source's position. Visualize the largest flat surface perpendicular to the light for the shadow's shape.

Question 2. Here are the shadows of some 3 -D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!)
(i) A circle
(ii) A square
(iii) A triangle
(iv) A rectangle
Answer:
(i) The given shadow that is a circle usually comes from a sphere.
(ii) The given shadow that is a square typically corresponds to a cube.
(iii) The given shadow that is a triangle is often cast by a cone.
(iv) The given shadow that is a rectangle could come from a cuboid or a cylinder.
In simple words: A round shadow is from a ball, a square shadow is from a block, a triangle shadow is from a cone, and a rectangle shadow can be from a box or a tube.

Exam Tip: Remember that shadows can sometimes be cast by multiple different 3D shapes, especially with varying light angles. Consider all possibilities.

Question 3. Examine if the following are true statements:
(i) The cube can cast a shadow in the shape of a rectangle.
(ii) The cube can cast a shadow in the shape of a hexagon.
Answer:
(i) The statement that a cube can cast a shadow in the shape of a rectangle is true. If you shine a light from an angle, a cube can certainly make a rectangular shadow.
(ii) The statement that a cube can cast a shadow in the shape of a hexagon is false. A cube cannot form a hexagonal shadow.
In simple words: A cube can make a rectangle shadow, which is true. But a cube cannot make a hexagon shadow, which is false.

Exam Tip: Experiment with a real cube and a light source. Observe that depending on the angle of the light, a cube can produce square, rectangular, or triangular shadows, but not a hexagon.