Volume
Category : 5th Class
Volume
In our daily life the number of things is stored in different kinds of container. Holding capacity of a container is called its volume. For ex.: The amount of water that a bucket can hold is called volume of the bucket.
Volume of the Cuboid
Volume of a cuboid = Length \[\times \] breadth \[\times \]height
=lbh.
In the cuboid ABCDEFG
Length of the cuboid = AB
Breadth of the cuboid = AE
Height of the cuboid = BC
Thus volume of the cuboid \[\text{ABCDEFG=AB }\!\!\times\!\!\text{ AE }\!\!\times\!\!\text{ BC=6 }\!\!\times\!\!\text{ 5 }\!\!\times\!\!\text{ 5=150 c}{{\text{m}}^{\text{2}}}\text{.}\]
Find the volume of the following cuboid:
Explanation
In the cuboid PQRSTUV
Length of the cuboid = PQ = 7 cm
Breadth of the cuboid = PT = 5 cm
Height of the cuboid = PS = 6 cm
Thus volume of the cuboid PQRSTUV \[\text{=PQ }\!\!\times\!\!\text{ PT }\!\!\times\!\!\text{ PS}\]
\[=\text{ }7\text{ }cm\times 5\text{ }cm\times 6\text{ }cm\text{ }=210\text{ }c{{m}^{3}}.\]
Volume of a Cube
Volume of a cube \[\text{= sid}{{\text{e}}^{\text{3}}}\text{.}\]
In the cube ABCDEFG
Volume of the cube ABCDEFG \[\text{A}{{\text{B}}^{\text{3}}}\text{=(8CM}{{\text{)}}^{\text{3}}}\text{=512C}{{\text{M}}^{\text{3}}}\]
Find the volume of the following figure:
Solution:
In the cube ABCDEFG
Volume of the cube ABCDEFG \[\text{=AB(6}\,\text{CM}{{\text{)}}^{\text{3}}}\text{=216}\,\text{c}{{\text{m}}^{\text{3}}}\]
Length of one side of an equilateral triangle is 4.3 cm. Find the perimeter of the triangle.
(a) 12.3cm
(b) 12.6cm
(c) 12.9cm
(d) 12.12cm
(e) None of these
Answer: (c)
Explanation
All three sides of an equilateral triangle are equal. Therefore, perimetre of the equilateral triangle\[~=4.3\text{ }cm\text{ }\times 3=12.9\]
Find the perimetre of the following figure:
(a) 14.5cm
(b) 16.5cm
(c) 18.5cm
(d) 20.5cm
(e) None of these
Answer: (b)
Explanation
Perimetre of the figure \[\text{=AB+BC+CD+DE+EA}\] \[\text{=3 cm+2 cm+2}\text{.5 cm+5 cm+4 cm=16}\text{.5 cm}\]
Find the length of third side of a triangle whose perimetre is 360 m and length of two sides are 150 m, and 110 m.
(a) 100m
(b) 110m
(c) 120m
(d) 130m
(e) None of these
Answer: (a)
The ratio of the sides of a triangle is 2 : 3 : 4 and its perimetre is 180 m. Find the length of each side.
(a) 40 m, 70 m, 80 m
(b) 40 m, 60 m, 80 m
(c) 50 m, 60 m, 80 m
(d) 40 m, 60 m, 100 m
(e) None of these
Answer: (b)
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Find the perimetre of the circle whose length of longest chord is 11.2 cm.
(a) 35.2cm
(b) 37.2cm
(c) 39.2cm
(d) 41.2cm
(e) None of these
Answer: (a)
Find the area of the square whose perimetre is 32 cm.
(a) \[32c{{m}^{2}}\]
(b) \[48c{{m}^{2}}\]
(c) \[64c{{m}^{2}}\]
(d) \[80c{{m}^{2}}\]
(e) None of these
Answer: (c)
Find the cost of painting a wall of 15 m long and 10 m wide, if the cost of painting is Rs 50 per\[100\text{ }{{m}^{2}}\]?
(a) Rs 60
(b) Rs 75
(c) Rs 90
(d) Rs 105
(e) None of these
Answer: (b)
In the following figure, ABCD is a rectangle. If 0 is the mid-point of the side AB. Find the area of the shaded region.
(a) \[40c{{m}^{2}}\]
(b) \[48c{{m}^{2}}\]
(c)\[~56c{{m}^{2}}\]
(d) \[56c{{m}^{2}}\]
(e) None of these
Answer: (b)
Find the area of the circle whose perimetre is 39.6 cm.
(a)\[120.74c{{m}^{2}}\]
(b) \[174.24c{{m}^{2}}\]
(c)\[147.74c{{m}^{2}}\]
(d) \[124.74c{{m}^{2}}\]
(e) None of these
Answer: (d)
Find the area of the rectangle whose perimeter and length are 36 cm and 12 cm respectively.
(a)\[70c{{m}^{2}}\]
(b) \[72c{{m}^{2}}\]
(c)\[78c{{m}^{2}}\]
(d) \[60c{{m}^{2}}\]
(e) None of these
Answer: (b)
Find the volume of the cube whose length of one side is 6.3 cm.
(a) \[250.47c{{m}^{3}}\]
(b) \[~250.074c{{m}^{3}}\]
(c) \[240.047c{{m}^{3}}\]
(d) \[\,250.047c{{m}^{3}}\]
(e) None of these
Answer: (d)
Find the volume of the cuboid whose length, breadth, and height are 5 cm, 7 cm and 7.5 cm respectively.
(a)\[258.5c{{m}^{3}}\]
(b)\[260.5c{{m}^{3}}\]
(c)\[262.5c{{m}^{3}}\]
(d)\[264.5c{{m}^{3}}\]
(e) None of these
Answer: (c)
A wall is to be constructed whose length, breadth and height will be 120 m, 10 m and 40 m respectively. If length, breadth and height of the brick are 4 cm, 3 cm and 2 cm respectively, how many bricks are required to construct the wall. (neget the volume of other materials used in the wall)
(a) 2000000000
(b) 2500000000
(c) 3000000000
(d) 3500000000
(e) None of these
Answer: (a)
Volume of a cuboid is \[\text{336 c}{{\text{m}}^{\text{3}}}\] . If length and breadth of the cuboid are 7 cm and 8 cm respectively. Find the height of the cuboid.
(a) 5cm
(b) 6cm
(c) 7cm
(d) 8cm
(e) None of these
Answer: (b)
A water tank can hold 12960000 litre of water. If length and breadth of the tank are 24 m and 20 m respectively. Find the height of the tank.
(a) 20m
(b) 24m
(c) 27m
(d) 30m
(e) None of these
Answer: (c)
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