VOLUME The unit for volume is cubic unit. Units depend on units of length, width, and height of that rectangular prism. To convert volume to one unit to another, look at the following example: For example, 1 metre equals 100 centimetres 1 m So, 1 cubic metre equals 100 x 100 x 100 cubic centimetres, which equals 1,000,000 cubic centimetres 1m 1m 100 cm There are some volume units that should be known. 100 cm 1 cubic centimetres equals 1 millilitres 1 litre equals 1,000 millilitres 1 litre equals 1,000 cubic centimetres 100 cm

Conversions 1 foot equals 30 centimetres 1 cubic foot equals 30 x 30 x 30 cubic centimetres equals 27,000 cubic centimetres 1 cubic foot equals 7.5 gallons 1 gallon equals 3,758.41 cubic centimetres (Fluid, US) 4,404.88 cubic centimemtres (Dry, US) 4,546.09 cubic centimemtres (UK)

Let’s do this! 1. Change the following volumes to litres. 1) A volume of 5,000 cubic centimetres ____________________ 2) A volume of 18,000 cubic centimetres ___________________ 3) A volume of 9,000 millilitres ________________ 4) A volume of 35,000 millilitres _______________ 5) A volume of 3 cubic metres _______________

Let’s do this! 2. Change the following volumes to cubic centimetres. 1) A volume 2,800 millilitres ____________________ 2) A volume of 3 litres _________________________ 3) A volume of 8 cubic metres _________________ 4) A volume of 3.2 litres ________________ 5) A volume of 0.25 cubic metres _______________

Example 1 To dig a pond in a rectangular shape with a width of 20 metres, length of 40 metres, and depth of 1.5 metres, what is the volume of soil dug in cubic metres? Method: Formula: Width x Length x Height (or Depth) So, volume of soil dug is 20 x 40 x 1.5 = 1,200 cubic metres. Answer: The volume of soil dug is 1,200 cubic metres.

Example 2 A water tank in a rectangular shape is 6 feet wide, 8 feet long and 10 feet high. What is the capacity of the water tank in gallons? Method: Formula: Width x Length x Height (or Depth) Volume of water tank = 6 x 8 x 10 = 480 cubic feet 1 cubic foot equals 7.5 gallons 480 cubic feet equal 480 x 7.5 gallons equals 3,600 gallons So, the water capacity of the water tank is 3,600 gallons. Answer: The water capacity of the water tank is 3,600 gallons.

Example 3 A water container with dimensions 25 x 30 x 60 cubic centimetres, had 15 litres used. What is the height of the water left in the container? Method: Formula: Width x Length x Height (or Depth) Volume of container = 25 x 30 x 60 = 45,000 cubic cm 15 litres of water were used 1 litre equals 1,000 cubic centimetres The water used equals 15 x 1,000 = 15,000 cubic cm The water left in the container equals 45,000 - 15,000

Example 3 Formula: Volume of water = Width x Length x Height (or Depth) 30,000 = 25 x 30 x h 25 x 30 x h = 30,000 h !\",\"\" h = $% & !\" = 40 centimetres The height of the water left in the container is 40 centimetres. Answer: The height of the water left in the container is 40 centimetres.

EXERCISE 2 1. Find the volume of the following three-dimensional geometric figures. 2. A pond is 25 metres wide, 40 metres long, and 20 metres deep. The volume of water in the pond is 14,000 cubic metres. What is the depth of the water surface from the top of the pond? 3. A glass rod in a rectangular shape has a cross section of 5.3 centimetres in width, and 8 centimetres in length. If its volume is 636 cubic centimetres, what is the height of the glass rod?

EXERCISE 2 4. A rectangular water container is 18 metres wide. The water leaked out from the container 270 cubic metres, and the water level decreased by 250 centimetres from the top of container. What is the length of the container? 5. A fish tank in a rectangular shape is 20 centimetres wide, 36 centimetres long and 30 centimetres high. What is the capacity of the fish tank in litres?

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