Visualising Solid Shapes Worksheet Page 7
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42UNIT-6
Note that in a 3D shape, diagonals connect two vertices
that do not lie on the same face.
E.g. the line segment from A to H in figure below is not
a diagonal for the solid. Diagonals must pass through
the inside of the shape. However, AH is diagonal of face
ADHE.
Example 11: Count the number of cubes in the given shapes.
Solution
: (i) 8 cubes
(ii) 6 cubes
Example 12 : Name the following polyhedrons and verify the Euler’s
formula for each of them.
(a)
(b)
(c)
Solution
: S. No Polyhedron
F
V
F + V
E
F + V –E
(a)
Tetrahedron
4
4
8
6
2
(b)
Cube
6
8
14
12
2
(c)
Pentagonal
7
10
17
15
2
prism
Volume, the space inside a three-dimensional object, is measured in cubic
unit. If the blocks you build are each 1 cubic unit, then the volume of a
block structure is equal to the number of blocks in the structure. For example,
a structure made from eight blocks has a volume of 8 cubic units. If the
3
blocks have an edge length of 1 cm, the structure’s volume is 8 cm
.
V V V V V
S S S S S
S S S S S
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ISUALISING
ISUALISING
OLID
OLID
HAPES
HAPES
ISUALISING
ISUALISING
ISUALISING
OLID
OLID
OLID
HAPES
HAPES
HAPES
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