a sewing box is 24cm by 18cm by 9cm. it is to be completely covered with silk material. what is the total surface to be covered?
the above figure is the volume, not the surface area. The box has 6 faces, in parallel pairs, of dimensions
24x18, 18x9, and 24x9
do those products and double their sum to get the total area.
24 * 18 * 9 = ?
To find the total surface area of the sewing box, we need to calculate the sum of the areas of all its sides.
Step 1: Calculate the area of each side of the box:
- The top and bottom sides have the same dimensions: 24cm by 18cm, so the area of each of these sides is 24cm * 18cm = 432cm².
- The front and back sides also have the same dimensions: 24cm by 9cm, so the area of each of these sides is 24cm * 9cm = 216cm².
- The left and right sides also have the same dimensions: 18cm by 9cm, so the area of each of these sides is 18cm * 9cm = 162cm².
Step 2: Determine the total surface area:
Since each side has its own area, we can sum up the areas to find the total surface area. In this case, we have 2 top/bottom sides, 2 front/back sides, and 2 left/right sides. Thus, the total surface area is:
2 * (432cm² + 216cm² + 162cm²) = 2 * 810cm²
Step 3: Simplify the calculation:
2 * 810cm² = 1620cm²
Therefore, the total surface area to be covered with silk material is 1620 square centimeters.
To find the total surface area of the sewing box, we need to calculate the area of each of its sides and then add them together.
The sewing box has six sides: a top, a bottom, two sides, and two ends.
The top and bottom covers have the same dimensions, so we only need to calculate one of them. The dimensions provided for the box are 24cm by 18cm, so the area of one cover is 24cm * 18cm = 432cm². Since there is a top and a bottom, the total area for these two sides is 432cm² * 2 = 864cm².
The sides of the box have dimensions of 24cm by 9cm, so the area of one side is 24cm * 9cm = 216cm². Since there are two sides, the total area for these two sides is 216cm² * 2 = 432cm².
The ends of the box have dimensions of 18cm by 9cm, so the area of one end is 18cm * 9cm = 162cm². Since there are two ends, the total area for these two ends is 162cm² * 2 = 324cm².
Now, let's sum up the areas of all the sides:
Top and bottom: 864cm²
Sides: 432cm²
Ends: 324cm²
Total surface area = 864cm² + 432cm² + 324cm² = 1620cm²
Therefore, the total surface area of the sewing box is 1620cm², which is the amount of silk material needed to completely cover it.