a paper box without a lid is 25 cm long. 16 cm wide and 5 cm deep . how many square centimetres of paper have been used to make the box .
Given,
Length of SQ. box= 25 cm
Width= 16 cm
Depth= 5 cm
Area of rectangle 1= 25×5
= 125 cm2
Area of rectangle 2= 25×5
=125 cm2
Area of rectangle 3= 16×5
=80 cm2
Area of rectangle 4= 16×5
=80 cm2
Area of rectangle 5= 16×25
=400 cm2
Total area of paper box= 400+80+80+125+125 = 810 cm2
(Note: Visualize a paper box consisting of 5 rectangles when laid out flat. Draw this and number the rectangles calculating the area of each separately using the formula 'Rectangle= length×breadth'. Add all the answers up and voila! The total area.)
visualize the box cut open and laid out flat on a table.
What do you see ?
Calculate the area of each of the 5 rectangles and add them up
Well, we can calculate the surface area of the box by adding up the areas of all its sides. Let's start with the bottom and the four sides:
Bottom: 25 cm x 16 cm = 400 cm²
Two long sides: 25 cm x 5 cm = 125 cm² each (since both are the same size)
Two short sides: 16 cm x 5 cm = 80 cm² each (again, they're equal)
Now, let's add them up:
Bottom: 400 cm²
Long sides: 125 cm² + 125 cm² = 250 cm²
Short sides: 80 cm² + 80 cm² = 160 cm²
Total surface area: 400 cm² + 250 cm² + 160 cm² = 810 cm²
Therefore, approximately 810 square centimeters of paper have been used to make the box. And by "approximately," I mean precisely. Because I'm a math genius. Or maybe I'm just full of hot air. Either way, 810 cm² it is! 🎈
To find the total surface area of the paper used to make the box without a lid, you need to calculate the surface area of each face and then add them together.
First, let's calculate the surface area of the longer sides of the box. These sides have a length of 25 cm and a height of 5 cm, so the surface area of each side is:
25 cm * 5 cm = 125 cm²
Since there are 2 longer sides, the total surface area of the longer sides is:
2 * 125 cm² = 250 cm²
Next, let's calculate the surface area of the shorter sides of the box. These sides have a width of 16 cm and a height of 5 cm, so the surface area of each side is:
16 cm * 5 cm = 80 cm²
And since there are 2 shorter sides, the total surface area of the shorter sides is:
2 * 80 cm² = 160 cm²
Finally, let's calculate the surface area of the bottom of the box, which has a length of 25 cm and a width of 16 cm:
25 cm * 16 cm = 400 cm²
Now, add up the surface areas of all the sides to find the total paper used:
250 cm² (longer sides) + 160 cm² (shorter sides) + 400 cm² (bottom) = 810 cm²
Therefore, 810 square centimetres of paper have been used to make the box.
To find out the number of square centimeters of paper used to make the box, we need to calculate the surface area of the box.
A box has six sides: a top, a bottom, a front, a back, and two sides. Since the box doesn't have a lid, we don't need to consider the top side.
The formula for calculating the surface area of a rectangular box is:
Surface Area = 2 * (Length * Width + Width * Depth + Length * Depth)
Let's plug in the given dimensions:
Length = 25 cm
Width = 16 cm
Depth = 5 cm
Surface Area = 2 * (25 * 16 + 16 * 5 + 25 * 5)
Surface Area = 2 * (400 + 80 + 125)
Surface Area = 2 * 605
Surface Area = 1210 cm²
Therefore, 1210 square centimeters of paper have been used to make the box.