A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid?
Behold the beauty of the metric system.
l litre of water has a mass of 1 kg and can be contained in a cube of 10cm by 10 cm by 10 cm or 1000 cm^3
so let the height of the cuboid be h cm
(12.5)(20)(h) = 1000
h = ....
H=1000/250=4cm
To find the height of the cuboid, we need to use the formula for the volume of a cuboid:
Volume = Length x Width x Height
We are given that the volume is 1 liter, which is equal to 1000 cubic centimeters (since 1 liter = 1000 cm^3).
So, we can write the equation as:
1000 cm^3 = 12.5 cm x 20 cm x Height
To find the height, we need to isolate it on one side of the equation.
Divide both sides of the equation by (12.5 cm x 20 cm):
Height = 1000 cm^3 / (12.5 cm x 20 cm)
Height = 1000 cm^3 / 250 cm^2
Height = 4 cm
Therefore, the height of the cuboid is 4 cm.
To find the height of the cuboid, we can use the formula for the volume of a cuboid, which is given by:
Volume = length × width × height
In this case, we are given the dimensions of the base (length and width), as well as the volume. We can rearrange the formula to solve for the height:
height = Volume / (length × width)
Given that the base dimensions are 12.5 cm and 20 cm, and the volume is 1 litre (1,000 cm³), we can substitute these values into the formula:
height = 1,000 cm³ / (12.5 cm × 20 cm)
To simplify the calculation, we can cancel out the units of cm³ and cm:
height = 1,000 / (12.5 × 20)
Now, we can calculate the height:
height = 1,000 / 250
height = 4 cm
Therefore, the height of the cuboid is 4 cm.