The shaded face of the cuboid is a square and has an area of 64 cm2. What is the volume of the cuboid that has a width of 17 cm? Can you plzz explain how you found you're answer.....
-THANX♥
If I am following your problem.
The area of ONE shaded face = 64 cm^2
Since, this face is a square, the length L equals the height h.
L = H
Cuboid SA = 2Lw + 2Lh + 2wh
Since you have the SA (surface area) of one face, and L = H,
SA = 2Lh
SA = 2LL (L = h)
64 = 2L^2
32 = L^2
L = (sqrt(32)) = 5.66 cm^2
Volume V = Lwh
L = 5.66
h = 5.66
w = 17
V = (5.66)(17)(5.66)
V = ?
You can finish this now.
I am not a tutor, but I think this is right.
To find the volume of a cuboid, we need to know the width, length, and height of the cuboid. In this case, we are given that the width is 17 cm, but we don't have any information about the length and height.
However, we have the additional information that the shaded face of the cuboid is a square with an area of 64 cm². Since the face is a square, this means that the length and height will be equal.
Let's call the length and height of the cuboid "x".
Now, we can use the formula for the area of a square to find x:
Area of a square = x * x = 64 cm²
Simplifying the equation, we have:
x^2 = 64
To solve for x, we can take the square root of both sides of the equation:
√(x^2) = √64
This gives us:
x = ±8
Since length and height cannot be negative, we can take the positive value of x, which is 8 cm.
Now that we know the length, width, and height of the cuboid, we can calculate the volume using the formula:
Volume of a cuboid = length * width * height
Volume = 8 cm * 17 cm * 8 cm
Volume = 1088 cm³
Therefore, the volume of the cuboid with a width of 17 cm is 1088 cm³.
To find the volume of the cuboid, we need to know its length, width, and height. However, we are given only the width of 17 cm and the area of the shaded face, which is a square with an area of 64 cm².
Since the shaded face is a square, the length of one side of the square is equal to the width of the cuboid. Therefore, the side length of the square face is also 17 cm. Since the area of a square is given by the formula A = side², we can find the length of the cuboid.
So, by substituting the side length of the square (17 cm) into the formula, we get:
64 cm² = 17 cm × 17 cm
To solve for the length of the cuboid, we rearrange the formula:
Length = √(Area of the shaded face)
Length = √64 cm²
Length = 8 cm
Now we have the length (8 cm), the width (17 cm), and we need to find the height to calculate the volume of the cuboid.
Unfortunately, the height of the cuboid is not given in the question. Without this information, it is impossible to determine the volume of the cuboid.