Volume of Cuboid
Total space occupied by a cuboid is called the volume of
cuboid. Volume of cuboid is given by the product of its area of base and the height of the cuboid.
Area of base is given by the product of its length and breadth. So the volume
of cuboid is given simply by the product of its length, breadth and height. i.e.
Volume of cuboid (V) = l×b×h
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Workout Examples
Example 1: Find the volume of the given solid figure.
Solution: Here, the given solid
figure is a cuboid of,
Length
(l) = 10cm
Breadth
(b) = 6cm
Height
(h) = 5cm
∴ Volume of cuboid (V) = l × b × h
= 10cm × 6cm × 5cm
= 300cm3
Example 2: A cuboid is twice as long as its breadth and 4cm high. If
its volume is 200cm3, find its length, breadth and total surface
area.
Solution: Let, breadth (b) = x
∴ length (l) = 2x
and, Height
(h) = 4cm
Volume of cuboid (V) = 200cm3
i.e. l × b × h = 200
or, 2x × x × 4 = 200
or, 8x2 = 200
or, x2 = 200/8
or, x2 = 25
or, x = 5cm
∴ length (l) =
2x = 2 × 5cm = 10cm
Breadth (b) = x = 5cm
∴ TSA = 2 (lb + bh + lh)
= 2 (10×5 + 5×4 + 10×4)
= 2 (50 + 20 + 40)
= 2 × 110
= 220cm2
Example 3: A rectangular piece of gold is 32cm long, 16cm broad and
8cm thick. If it is melted and made a cube, find the total surface area of the
cube.
Solution: Here, Length of
rectangular piece of gold (l) = 32cm
Breadth of rectangular piece of
gold (b) = 16cm
Height of rectangular piece of gold
(h) = 8cm
∴ Volume of rectangular
piece of gold (V) = l × b × h
= 32cm × 16cm × 8cm
= 4096cm3
Since rectangular piece of gold
is melted to form a cube,
∴ Volume of cube = Volume of
rectangular piece of gold
i.e. l3 = 4096cm3
or, l3 = (16cm)3
∴ l = 16cm
Now,
TSA of cube = 6l2
= 6 × (16cm)2
= 6 × 256cm2
= 1536cm2
You can comment your questions or problems
regarding the area and volume of cuboid here.
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