Three cubes of volume 343 cubic cm are joined end to end.find surface area and volume of the resulting cuboid.
Well, the volume is simply 3 times one of the cubes.
For the surface area, think of what you would see.
Wouldn't 4 faces not be visible ?
To find the surface area and volume of the resulting cuboid formed by joining three cubes, let's go step by step:
Step 1: Find the side length of each cube.
Since the volume of each cube is given as 343 cubic cm, we can find the side length (s) of the cube using the formula:
Volume of a cube = side length^3
343 = s^3
Taking the cube root of both sides, we get:
s = ∛343
s = 7 cm
Step 2: Find the dimensions of the resulting cuboid.
When the cubes are joined end to end, the resulting shape is a cuboid with dimensions of 3s by s by s.
Therefore, the dimensions of the resulting cuboid are:
Length = 3s = 3(7) cm = 21 cm
Width = s = 7 cm
Height = s = 7 cm
Step 3: Find the surface area of the resulting cuboid.
The surface area of a cuboid can be found using the formula:
Surface Area = 2(Length x Width + Width x Height + Height x Length)
Substituting the values, we have:
Surface Area = 2(21 x 7 + 7 x 7 + 7 x 21)
Surface Area = 2(147 + 49 + 147)
Surface Area = 2(343)
Surface Area = 686 square cm
Step 4: Find the volume of the resulting cuboid.
The volume of a cuboid can be found using the formula:
Volume = Length x Width x Height
Substituting the values, we have:
Volume = 21 x 7 x 7
Volume = 1029 cubic cm
Therefore, the surface area of the resulting cuboid is 686 square cm, and the volume is 1029 cubic cm.
To find the surface area of the resulting cuboid, we need to find the dimensions of the joined cubes.
Given that the volume of each cube is 343 cubic cm, we can calculate the length of the side of each cube by finding the cube root of the volume.
The formula to find the side length (S) of each cube is S = V^(1/3), where V is the volume of each cube.
Therefore, S = 343^(1/3) = 7 cm.
Since we have three cubes joined end to end, the resulting cuboid will have a length of 3 times the side length of each cube, which is 3 * 7 cm = 21 cm.
The width and height of the resulting cuboid will be equal to the side length of each cube, which is 7 cm.
Now, we can calculate the surface area (A) of the resulting cuboid using the formula A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
Substituting the values, we get A = 2(21 * 7) + 2(21 * 7) + 2(7 * 7) = 882 + 882 + 98 = 1862 square cm.
So, the surface area of the resulting cuboid is 1862 square cm.
To find the volume of the resulting cuboid, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Substituting the values, we get V = 21 * 7 * 7 = 1029 cubic cm.
Therefore, the volume of the resulting cuboid is 1029 cubic cm.
since 343=7^3 the cubes are 7 cm on a side
By joining them, 4 faces are hidden. Each cube has 6 faces.
So, the remaining surface area is 3*(6*7^2)-4*7^2 = 686 cm^2