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 how much cardboard (the area)bis needed to make a single milk carton

Answer 1

To calculate the total area of cardboard needed for the carton, we need to find the area of both the base and the four semi circular flaps.

1. Base of the carton:
The area of the square base is calculated by multiplying the length and width:
Area of base = 6cm * 6cm = 36 sq cm

2. Semi circular flaps:
Each semi circular flap has a radius of 3cm. The area of one semi circular flap can be calculated as half the area of a full circle with radius 3cm:
Area of one semi circular flap = 1/2 * π * (3cm)^2 = 4.5π sq cm

Since there are four semi circular flaps in the carton, the total area of all four flaps is:
Total area of all four flaps = 4 * 4.5π = 18π sq cm

3. Total area of cardboard needed:
The total area of cardboard needed to make a single milk carton is the sum of the area of the base and the total area of the four flaps:
Total area = Area of base + Total area of all four flaps
Total area = 36 sq cm + 18π sq cm ≈ 36 + 56.55
Total area ≈ 92.55 sq cm

Therefore, approximately 92.55 sq cm of cardboard is needed to make a single milk carton.