The base of a one litre carton of milk is 8cms x 8cms. What must be its minimum height?
To determine the minimum height of the one-litre carton of milk, we need to calculate the volume of the carton.
Given: The base of the carton is 8 cm x 8 cm.
To find the volume of the carton, we multiply the area of the base by the height of the carton.
Area of the base = length x width = 8 cm x 8 cm = 64 cm²
Since the volume of the carton is 1 litre, we convert it to cubic centimeters (1 L = 1000 cm³).
Volume of the carton = 1 L = 1000 cm³
Therefore, 1000 cm³ = 64 cm² x height of the carton.
Simplifying the equation: 1000 cm³ = 64 cm² × height.
To find the minimum height, we rearrange the equation:
Height = 1000 cm³ / 64 cm²
Height ≈ 15.63 cm (rounded to two decimal places)
Thus, the minimum height of the one-litre carton of milk must be approximately 15.63 cm.