a cuboid has a diagonal of lenght 9cm and a square base of side 4cm. what is its height
diagonal= sqrt(4^2+4^2 + h^2)
9^2=2*16+h^2
solve for h
To find the height of the cuboid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In the case of the cuboid, the diagonal acts as the hypotenuse, and the sides of the base form a right-angled triangle.
Let's label the length, width, and height of the cuboid as follows:
Length = l
Width = w
Height = h
We are given that the side of the square base is 4 cm, so the length and width are both 4 cm.
We are also given that the diagonal has a length of 9 cm.
Using the Pythagorean theorem, we can write the equation:
l^2 + w^2 + h^2 = diagonal^2
Substituting the known values, we have:
4^2 + 4^2 + h^2 = 9^2
Simplifying the equation, we get:
16 + 16 + h^2 = 81
Combining like terms:
32 + h^2 = 81
Subtracting 32 from both sides:
h^2 = 81 - 32
h^2 = 49
Taking the square root of both sides:
h = √49
h = 7 cm
Therefore, the height of the cuboid is 7 cm.
To find the height of the cuboid, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the cuboid acts as the hypotenuse of a right-angled triangle. One side of the triangle is the height of the cuboid, and the other side is the length of the diagonal. So, we can set up the equation:
diagonal^2 = height^2 + base^2
Given that the diagonal is 9 cm and the base is 4 cm, we can substitute these values into the equation:
9^2 = height^2 + 4^2
81 = height^2 + 16
Next, let's isolate the height^2 term:
height^2 = 81 - 16
height^2 = 65
Finally, we take the square root of both sides to find the height:
height = √65
Using a calculator, we can find the approximate value of the square root of 65 as 8.06 cm.
Therefore, the height of the cuboid is approximately 8.06 cm.