## S. K. Gupta Anubhuti Gangal Class 5 Math Sixteenth Chapter Volume Exercise 54

## EXERCISE 54

**(1) Find the volume of each solid and write the unit with your answer.**

Solution: (a) Volume = (12 × 12 × 10) cu cm = 1440 cu cm

(b) Volume = (2.1 × 5 ×1.2) cu cm = 12.6 cu cm

(c) Volume = (3.8 × 2 × 5) cm^{3} = 38 cm^{3}

(d) Volume = (1.2 × 1.2 × 1.2) cm^{3} = 1.728 cm^{3}

**(2) For a cuboid, copy and complete the table:**

**(3) Find the volume of the following cubes:**

(a) Edge 4 cm

Solution: Volume = (4 × 4 × 4) cu cm = 64 cu cm

(b) Edge 5 cm

Solution: Volume = (5 × 5 × 5) cu cm = 125 cu cm

(c) Edge 1.1 cm

Solution: Volume = (1.1 × 1.1 × 1.1) cu cm = 1.331 cu cm

(d) Edge 70 mm

Solution: Volume = (70 × 70 × 70) cu cm = 343000 cu cm

(e) Edge 80 mm

Solution: Volume = (80 × 80 × 80) cu mm = 512000 cu mm

(f) Edge 4.3 m

Solution: volume = (4.3 × 4.3 × 4.3) cu m = 79.507 cu m

**(4) A 100-centimeter cube is the same size as a 1-meter cube. How many cubic centimeters make 1 cubic meter?**

Solution: Volume of 1 cubic meter = (100 × 100 × 100) cu cm = 1000000 cu cm

**(5) Which has the greater volume: box that measure 10 cm by 6 cm by 4 cm or one that measures 6 cm by 6 cm by 7 cm?**

Solution: Volume of first box = (10 × 6 × 4) cu cm = 240 cu cm

Volume of second box = (6 × 6 × 7) cu cm = 252 cu cm

**(6) A heap of wood is pile 5 dm wide, 9 dm long, and 3 dm high. What is the volume of the heap of wood?**

Solution: The required volume of the heap = (5 × 9 × 3) cu dm = 135 cu dm

**(7) Find the volume of rectangular solids whose dimensions are as followers:**

(a) Length 15 m, breadth 12 m, thickness 75 cm.

Solution: Here, Thickness = 75 cm = 0.75 m

Hence, volume = (15 × 12 × 0.75) cu m = 135 cu m

**(8) Calculate the volume of air in six-room house, if the height of each room is 3 m, and the length and widths of the rooms, in meters, are as given by following table:**

Solution: Volume of room A = (9 × 5 × 3) m^{3} = 135 m^{3}

Volume of room B = (4 × 4 × 3) m^{3} = 48 m^{3}

Volume of room C = (5 × 6 × 3) m^{3} = 90 m^{3}

Volume of room D = (6 × 4 × 3) m^{3} = 72 m^{3}

Volume of room E = (8 × 4 × 3) m^{3 }= 96 m^{3}

Volume of room F = (3 × 2 × 3) m^{3} = 18 m^{3}

Hence, the total volume is 459 cu m.

**(9) Sameer has 80 one-centimeter cubs. Which of these cuboids could he build?**

(a) 6 cm long, 5 cm wide, 4 cm high

Solution: Volume = (6 × 5 × 4) cu cm = 120 cu cm

(b) 8 cm long, 5 cm wide, 2 cm high

Solution: Volume = (8 × 5 × 2) cu cm = 80 cu cm

(c) 10 cm long, 4 cm wide, 5 cm high

Solution: volume = (10 × 4 × 5) cu cm = 200 cu cm

(d) 6 cm long, 7 cm wide, 2 cm high

Solution: Volume = (6 × 7 × 2) cu cm = 84 cm

(e) 7 cm long, 5 cm wide, 2 cm high

Solution: Volume = (7 × 5 × 2) cu cm = 70 cu cm

(f) 10 cm long, 4 cm wide, 2 cm high

Solution: Volume = (10 × 4 × 2) cu cm = 80 cu cm

**(10) Write the length, breadth and height and a cube has an edge of 6 cm. Which one has greater volume?**

**(11) A cuboid is 6 cm long, 3 cm wide and 3 cm high and cube has an edge of 6 cm. Which one has greater volume?**

Solution: Volume of the cuboid = (6 × 3 × 3) cu cm = 54 cu cm

Ans volume of the cube = (6 × 6 × 6) cu cm = 216 cu cm

**(13) The floor of a class room is shaped as shown on the right.**

(a) What is the perimeter of the floor?

Solution: Perimeter of the floor = [2 × (15+10)] m = (2 × 25) m = 50 m

(b) What is the floor area of the room?

Solution: Area of the floor = (15 × 10) sq m = 150 sq m

(c) If the height of the room is 8 m, how many cubic meters of space is in the room?

Solution: The required cubic meters = (15 × 10 × 8) cu m = 1200 cu m

**(14) One centimeter, one square centimeter and one cubic centimeter are different measurements. Why?**

Ans: One centimeter denotes length, one square centimeter denotes area and one cubic centimeter denotes volume.

** (15) A trench was 30 m long, 2 m wide and 2 m deep. How many cubic meters of earth were removed to dig the trench?**

Solution: The required cubic meters = (30 × 2 × 2) cu m = 120 cu m

**(16) ****Complete the following table:**

Solution: (a) Height = [24 ÷ (4 × 2)] cm = 3 cm

(b) Height = [30 ÷ (5 × 3)] cm = 2 cm

(c) Length = [2100 ÷ (70 × 5)] mm = 6 mm

(d) Breadth = [2.4 ÷ (8 × 0.5)] cm = 0.6 cm

(e) Length = [1.04 ÷ (4 × 0.05)] mm = 5.2 mm