what volume of paint will be needed to paint the prism box that has a width, length and height of 6cm if about 100ml of paint needed to cover 1 square metre per coating.
N.B for the purpose of durability of the packaging, the paint should be applied on the interior and the exterior of the packaging including underneath
To find the volume of paint needed to cover the prism box, we need to calculate the surface area of all the faces of the box and then multiply it by the number of coatings.
The prism box has 6 faces, each with an area of 6 cm x 6 cm = 36 square cm.
To convert this to square meters, divide by 10,000:
36 square cm ÷ 10,000 = 0.0036 square meters.
Since there are 6 faces, the total surface area of the box is 6 x 0.0036 square meters = 0.0216 square meters.
If 100 ml of paint is needed to cover 1 square meter per coating, then for 0.0216 square meters, we would need 0.0216 square meters x 100 ml = 2.16 ml of paint for one coating.
However, since the paint needs to be applied on both the interior and exterior of the packaging, including underneath, we need to double this amount.
Therefore, the total volume of paint needed for one coating would be 2.16 ml x 2 = 4.32 ml.
Please note that this calculation assumes the prism box has no lid or bottom and only has six faces. If the box is more complex or has additional surfaces, the calculation may differ.
To calculate the volume of paint needed to paint the prism box, we need to find the total surface area of the box.
The surface area of a prism with a rectangular base can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height of the prism.
In this case, the width, length, and height are all 6cm. Plugging these values into the formula, we get:
Surface Area = 2(6)(6) + 2(6)(6) + 2(6)(6)
Surface Area = 72 + 72 + 72
Surface Area = 216 square cm
Since we need to paint the interior, exterior, and underneath of the packaging, we will need to multiply the surface area by the number of sides:
Total Surface Area = 216 * 6
Total Surface Area = 1296 square cm
Now, since 100ml of paint is needed to cover 1 square meter per coating, we need to convert our surface area from square cm to square meters:
Total Surface Area (in square meters) = 1296 / 10000
Finally, multiply this value by 100ml to find the volume of paint needed:
Volume of Paint = Total Surface Area (in square meters) * 100ml
Thus, the volume of paint needed to paint the prism box is the final answer.