5th Class Mathematics Area, Perimeter and Volume Volume

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 \[\text{=AB(6}\,\text{CM}{{\text{)}}^{\text{3}}}\text{=216}\,\text{c}{{\text{m}}^{\text{3}}}\]  

 

 

  • If base of triangle is doubled, the area of the triangle also gets doubled.
  • If area and perimeters of a circle are numerically equal, numeric value of the radius of the circle is 2.  

 

 

  • Perimeter is defined as the length the length of boundary line of a close geometrical figure.
  • Perimeter of a triangle is defined as the sum of all three sides.
  • Perimeter of an equilateral triangle is given by 3 \[\times \] length of a side.
  • Perimeter of a rectangle is given by 2 (length + breadth).
  • Perimeter of a square is given by 4\[\times \] side.
  • Space occupied by an object is called area.
  • Area of square is given by \[\text{sid}{{\text{e}}^{\text{2}}}\text{.}\]
  • Holding capacity of a container is called volume.

 

 

   

 

  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)  

 
 

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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