Volume

What Do We Mean By Volume

What do we mean by volume?

- the amount of space that a substance or object occupies or that is enclosed within a container.

How do we measure it?

- In math, the volume is the amount of space in a certain 3D object. For example, a fish tank has 3 feet in length, 1 foot in width, and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet.

Is there a conversion to liters?

- A liter is a cubic decimetre, which is the volume of a cube 10 centimeters × 10 centimeters × 10 centimeters (1 L ≡ 1 dm3 ≡ 1000 cm3). Hence 1 L ≡ 0.001 m3 ≡ 1000 cm3 and 1 m3 (i.e. a cubic meter, which is the SI unit for volume) is exactly 1000 L.

The volume of a rectangle

- To find the volume of a rectangle, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

The volume of a cylinder

- A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r²

The volume of a prism 

-Volume of a rectangular prism = (length x width x height) cubic units. V = (l x w x h) cubic units

The volume of a barrel

- Formula. Barrel Volume = πh12 (2D² + d²

The volume of a cone

There is a kiddy pool in the back garden it is 3 meters wide 8 meters long and we can only fill it 1.2m high.

- How much water does it take to full?

to calculate I use 

lxbxh

3 x 8 x l.2 = 28.8

I know that 1m3 = 1 liter = 1000cm3

28.8 x 1000 = 28800 liter

-the pool is on a deck how heavy is it?

3m x 8m x 1.2m = 28.8M3

1l = 1kg

28.8 x 1000 = 28800kg

There is a trailer of barrels 

Each barrel is 1.5m high with a diameter of 0.75m

how much weight is on the trailer

0.75/2 = 0.375

3.142 x 0.375 x 2 = 2.3565m2

2.3565 x 1000 - 2356.5

2356.5 x 6 = 14139L

M3

Cm3

Mm3