**Category : **5th Class

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)**

*play_arrow*Area and Perimeter*play_arrow*Introduction*play_arrow*Perimeter*play_arrow*Area*play_arrow*Volume

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