Given that the volume of the cuboid is equal to 72 cm³
The length of the cuboid is equal to 6 cm and the height is equal to half the length.
Calculate the surface of the cuboid
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Given that the volume of the cuboid is equal to 72 cm³
The length of the cuboid is equal to 6 cm and the height is equal to half the length.
Calculate the surface of the cuboid
The first step is to calculate the relevant data for all the components of the box.
The length of the box = 6
Given that the height of a cuboid is equal to half its length we are able to deduce the height of the box as follows : 6/2= 3
Hence the height = 3
In order to determine the width, we insert the known data into the formula for the volume of the box:
height*length*width = volume of the cuboid.
3*6*width = 72
18*width=72
We divide by 18:
Hence the width = 4
We are now able to return to the initial question regarding the surface of the cuboid.
Remember that the formula for the surface area is:
(height*length+height*width+length*width)*2
We insert the known data leaving us with the following result:
(3*6+4*3+4*6)*2=
(12+24+18)*2=
(54)*2=
108
108 cm²
Identify the correct 2D pattern of the given cuboid:
The surface area formula requires length, width, AND height. Since you only know length (6 cm) and that height = length/2 = 3 cm, you must use the volume formula to find the missing width before calculating surface area.
Surface area is the total area of all faces of the 3D shape. A cuboid has 6 faces: top/bottom, front/back, and left/right sides. Each pair has the same area, so we calculate 3 different areas and multiply by 2.
Use for volume (space inside). Use for surface area (covering the outside). Think: volume fills it up, surface area wraps it up!
Yes! You could find height first (6 ÷ 2 = 3), then width (72 ÷ 18 = 4), then surface area. The key is having all three dimensions before using the surface area formula.
That's fine! Work with exact fractions or decimals until the final step. Just make sure your arithmetic is careful, especially when the width comes out as a fraction.
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