1.A RECTANGULAR BOX IS TO BE PAINTED ON ALL ITS SIDES. IF THE BOX IS 15 DM LONG, 12 DM WIDE AND 6 DM HIGH. HOW MUCH SURFACE IS TO BE PAINTED ?
2. IF EACH SIDE OF AN OPEN CUBICLE BOX IS 2X+3 CM. FIND ITS TOTAL SURFACE AREA.
3. MICHEAL IS TO MAKE A BOX IN THE FORM OF A RECTANGULAR PRISM. HOW MUCH CARTOON WILL HE NEED IF THE PRISM IS TO BE 32 CM HIGH WHILE ITS BASE IS TO BE 12 CM AND 18 CM.
Total surface area of a rectangular box
=2(lw+wh+hl)
where l,w,h=length, width and height respectively.
Total surface area of a cubical box (all sides equal to "a"
=6a²
Total surface area of a Rectangular prism : see above for rectangular box
1. To calculate the surface area of a rectangular box, you need to find the area of each side and then add them together.
First, let's find the area of the four sides of the box:
- Two sides measure 15 dm (length) by 6 dm (height), so the area of both sides is 15 dm * 6 dm = 90 dm².
- The other two sides measure 12 dm (width) by 6 dm (height), so the area of both sides is 12 dm * 6 dm = 72 dm².
Next, let's find the area of the top and bottom of the box:
- The top area measures 15 dm (length) by 12 dm (width), so the area is 15 dm * 12 dm = 180 dm².
- The bottom area is the same as the top area, so it is also 180 dm².
Now, add up all these areas to get the total surface area:
90 dm² + 72 dm² + 180 dm² + 180 dm² = 522 dm².
Therefore, the total surface area to be painted is 522 dm².
2. To find the total surface area of an open cubicle box, you need to find the area of each side and then add them together.
A cubicle box has six sides. Let's call each side A, B, C, D, E, and F.
- Side A and side B are the same and measure 2x + 3 cm (length) by 2x + 3 cm (width), so the area of both sides is (2x + 3 cm) * (2x + 3 cm) = (2x + 3)² cm².
- Side C and side D are also the same and measure 2x + 3 cm (width) by 2x + 3 cm (height), so the area of both sides is (2x + 3 cm) * (2x + 3 cm) = (2x + 3)² cm².
- Side E and side F are the same and measure 2x + 3 cm (length) by 2x + 3 cm (height), so the area of both sides is (2x + 3 cm) * (2x + 3 cm) = (2x + 3)² cm².
Now, add up all these areas to get the total surface area:
2 * (2x + 3)² cm² + 2 * (2x + 3)² cm² + 2 * (2x + 3)² cm²
= 4 * (2x + 3)² cm² + 4 * (2x + 3)² cm² + 2 * (2x + 3)² cm²
= 10 * (2x + 3)² cm².
Therefore, the total surface area of the open cubicle box is 10 * (2x + 3)² cm².
3. To find the amount of cardboard needed for a rectangular prism, you need to calculate the surface area of the prism.
The surface area of a rectangular prism is the sum of the areas of its six faces.
For this prism, we have:
- The top and bottom face are the same and measure 12 cm (width) by 18 cm (length), so the area of both faces is 12 cm * 18 cm = 216 cm² each.
- The front and back faces are the same and measure 32 cm (height) by 18 cm (length), so the area of both faces is 32 cm * 18 cm = 576 cm² each.
- The left and right faces are the same and measure 12 cm (width) by 32 cm (height), so the area of both faces is 12 cm * 32 cm = 384 cm² each.
Now, add up all these areas to get the total surface area:
216 cm² + 216 cm² + 576 cm² + 576 cm² + 384 cm² + 384 cm² = 2352 cm².
Therefore, Michael will need 2352 cm² of cardboard to make the rectangular prism.