Prism
A solid object in which two opposite faces are congruent
and parallel and its cross section part is congruent to its bases is called a
prism. For example: cube, cuboid, cylinder etc are prisms. In the figure given below is a cuboid (prism).
The name of prism is
determined with respect to its base.
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Cuboid:
A rectangular prism is called a cuboid. A cuboid is also
known as a rectangular parallelopiped.
Cross
sectional area = Area of base
= l × b
Total
surface area = Area of all 6 faces of the cuboid
= lb+lb+bh+bh+lh+lh
= 2lb + 2bh + 2lh
= 2(lb + bh + lh)
Volume
= Area of base × height
= l × b × h
Cube:
A cuboid in which all three dimensions (length, breadth
and height) are equal is called a cube.
∴ Cross-sectional
area = Area of base = l2
Total surface area = 6l2
Volume = l3
Cylinder:
A circular prism is called a cylinder.
∴ Cross-sectional
area = Area of base = Area of circle = πr2
Total surface area = Curved surface
area + area of two bases (circles) = 2Ï€rh + 2Ï€r2
Volume = Area of base × height = Ï€r2h
Triangular Prism:
A prism having its base a
triangular shaped is called a triangular prism.
Lateral surface area = Perimeter of Δ
× height = Ph
Total surface area = Lateral surface area + Area of 2 bases = Ph +
2A
Volume = Area of base triangle ×
height = Ah
Workout Examples
Example 1: Find the area of cross-section, total surface area and
volume of the given prism.
Solution: The given prism is a
cuboid of,
Length
(l) = 8cm
Breadth
(b) = 6cm
Height
(h) = 12cm
∴ Area of cross section = l × b
= 8cm × 6cm
= 48cm2
Total surface area = 2(lb+bh+lh)
= 2(8×6 + 6×12 + 8×12)
= 2(48 + 72 + 96)
= 2 × 216
= 432cm2
Volume = l × b × h
= 8cm
× 6cm × 12cm
= 576cm3
Example 2: Find the cross-section area, total surface area and the volume of the given prism.
Solution: The given prism is a
cube of,
Length
(l) = 8cm
∴ Area of cross section = l2
= (8cm)2
= 64cm2
Total surface area = 6l2
= 6 × (8cm)2
= 6 × 64cm2
= 384cm2
Volume = l3
= (8cm)3
= 512cm3
Example 3: Find the area of cross-section, total surface area and
volume of the given prism.
Solution: The given prism is a
cylinder of,
Radius
(r) = 7cm
Height
(h) = 12cm
∴ Area of cross section = Ï€r2
= 22/7 × 72
= 154cm2
Total surface area = 2Ï€rh + 2Ï€r2
= 2 × 22/7 × 7 × 12 + 2 × 22/7 × 72
= 528 + 308cm2
= 836cm2
Volume = πr2h
= 22/7 × 72 × 12
= 1848cm3
Example 4: Find the area of cross-section, total surface area and
volume of the given prism.
Solution: The given figure is a
triangular prism with right angled triangle base of,
base
(b) = 4cm, perpendicular (p) = 3cm
∴ Perimeter =
4cm + 3cm + 5cm = 12cm
Height
of prism (h) = 10cm
∴ Area of cross section (A) = Area of right
angled triangle
= ½
× b × h
= ½
× 4 × 3
= 6cm2
Total surface area = Ph + 2A
= 12cm × 10cm + 2 × 6cm2
= 120cm2 + 12cm2
= 132 cm2
Volume = A × h
= 6cm2 × 10cm
= 60cm3
Example 5: Find the area of cross-section, total surface area and
volume of the given prism.
Solution: Base is divided into two parts A1 and A2 as given below in the figure,
∴ Area of cross section (A) = A1 + A2
= 5
× 3 + 4 × 2
= 15
+ 8
= 23cm2
Total surface area = Perimeter of
cross-section × h + 2 × cross-section area
= (5 + 3 + 3 + 4 + 2 + 7) × 8 + 2 × 23
= 24 × 8 + 46
= 192 + 46
= 238cm2
Volume = A × h
= 23cm2 × 8cm
= 184cm3
You can comment your questions or problems
regarding the surface area and volume of prisms here.
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