Exercise 13.1
1. Draw the following 3-D figures on isometric dot sheet.
(i).
Solution
(ii).
Solution:
(iii).
Solution
(iv).
Solution
1. Draw a cuboid on the isometric dot sheet with the measurements 5 units × 3 units × 2 units.
Solution
Find the number of unit cubes in the following 3-D figures.
Solution
Figure (i):
Base: The "L" shape at the bottom has
Top: There are
Total:
Figure (ii):
Center: There's 1 cube in the middle.
Arms: Four arms extend from the center, each with
Total: 1 (center) + (4 arms x
Figure (iii):
Bottom Layer (Base): A 3 x 3 square with
Middle Layer: A 2x2 square with
Top Layer:
Hidden Layer: 6 cubes at the base that are not visible.
Total:
Figure (iv):
Bottom Layer (Base): A 3x3 square with
Middle Layer: A 2x2 square with
Top Layer:
Total: 9 (bottom) + 4 (middle) + 1 (top) =
4. Find the areas of the shaded regions of the 3-D figures given in question number 3.
Solution
Figure (i):
Front: The front face of the base "L" has
Side: There is
Total:
Figure (ii):
Each Arm: Each of the four arms has 2 squares shaded on its top surface.
Center: The center cube has 1 square shaded on top.
Total: (4 arms x
Figure (iii):
Bottom Layer (Base): The top surface of the base has
Middle Layer: The top surface of this layer has
Top Layer: The top surface has
Sides of the Base: There are
Total: 9 (base) + 4 (middle) + 1 (top) + 3 (sides) =
Figure (iv):
Bottom Layer (Base): The top surface of the base has
Middle Layer: The top surface of this layer has
Top Layer: The top surface has
Total: