The base of a square. 6cm by 6cm. The height of the carton is 10cm.four overlapping semi circular flaps seal the top of the carton.each with a radius of 3cm. Determine the capacity of the carton in litres
First, calculate the area of the square base:
Area of square base = side x side
Area of square base = 6cm x 6cm
Area of square base = 36 cm²
Next, calculate the area of each semi-circular flap:
Area of semi-circular flap = 1/2 x π x radius²
Area of semi-circular flap = 1/2 x π x 3cm x 3cm
Area of semi-circular flap = 4.5π cm²
Since there are four semi-circular flaps, the total area of the flaps is:
Total area of flaps = 4 x 4.5π cm²
Total area of flaps = 18π cm²
The total volume of the carton is:
Volume = Area of square base x Height + Total area of flaps
Volume = 36 cm² x 10 cm + 18π cm²
Volume = 360 cm³ + 18π cm²
Volume = 360 cm³ + 56.55 cm³
Volume = 416.55 cm³
Finally, convert the volume to litres:
1 litre = 1000 cm³
Volume = 416.55 cm³ ÷ 1000
Volume = 0.41655 litres
Therefore, the capacity of the carton is 0.41655 litres.