four cubes of volume 125cm3 are joined end to end .find the volume and surface area of the resulting cuboid
make a sketch of visualize what you see
I see two end cubes with 5 faces showing and 2 cubes in the middle with only 4 faces showing
one cube has volume of 125, so each side is 5
(since 5^3 = 125)
so the surface area of one face = 25 cm^2
and we have 2(5) + 2(4) or 18 faces
so the total exposed surface area = 25(18) = 450 cm^2
the volume of the 4 cubes of course is simply 4(125) or 500 cm^3
To find the volume of the resulting cuboid, we need to calculate the total volume of the four cubes when joined end to end.
The volume of one cube is given as 125 cm^3. Since there are four cubes, the total volume will be:
Total Volume = (Volume of one cube) × (Number of cubes)
= 125 cm^3 × 4
= 500 cm^3
Therefore, the volume of the resulting cuboid is 500 cm^3.
To find the surface area of the resulting cuboid, we need to calculate the area of each face and sum them up.
A cuboid has six faces - top, bottom, front, back, left, and right.
The surface area of each cube is equal to the sum of the areas of these six faces.
Area of one face = length × width
Since the cubes are 3D, the length, width, and height of each cube are the same, which we'll denote as a.
Therefore, the surface area of one cube is:
Surface Area of one cube = 6a^2
For the resulting cuboid, we'll have four cubes joined end to end. So the total surface area of the resulting cuboid will be:
Total Surface Area = (Surface Area of one cube) × (Number of cubes)
= 6a^2 × 4
= 24a^2
To find the surface area, we need the value of "a". However, the problem doesn't provide that information. If you have the value of "a" or any other relevant details, I can help you further.
To find the volume of the resulting cuboid, we need to determine the dimensions of the cuboid based on the cubes joined end to end.
Since each cube has a volume of 125 cm³, and there are four cubes joined end to end, the total volume of the resulting cuboid will be 125 cm³ x 4 = 500 cm³.
To find the dimensions of the cuboid, we need to consider that the cubes are joined end to end. Therefore, the height (h) of the resulting cuboid will be the same as the side length of the cube, which is 125^(1/3) = 5 cm.
The width (w) and length (l) of the cuboid will be the sum of the side lengths of the cubes. Since each cube has a side length of 5 cm, the total width and length of the cuboid will be 5 cm + 5 cm + 5 cm + 5 cm = 4 x 5 cm = 20 cm.
Therefore, the resulting cuboid has dimensions of 20 cm x 5 cm x 5 cm. Hence, the volume is 20 cm x 5 cm x 5 cm = 500 cm³.
To find the surface area of the resulting cuboid, we need to calculate the area of each face and then add them up.
The cuboid has six faces. The bottom and top faces both have an area of 20 cm x 5 cm = 100 cm². The two side faces each have an area of 20 cm x 5 cm = 100 cm². The two end faces (front and back) each have an area of 5 cm x 5 cm = 25 cm².
Adding up all the areas, we get 100 cm² (bottom) + 100 cm² (top) + 100 cm² (side) + 100 cm² (side) + 25 cm² (front) + 25 cm² (back) = 450 cm².
Therefore, the surface area of the resulting cuboid is 450 cm².