A cuboid has a diagonal of length 9 cm and a square base of side 4cm. What is its height?
Find the diagonal of the base using Pythagoras, call it d
Let the height of the cuboid be h.
Then the diagonal of the base and the height form a right-angled
triangle with hypotenuse 9.
that is: h^2 + d^2 = 9^2 , you have d^2 from the first part, solve for h
To find the height of the cuboid, we can use the Pythagorean theorem. The diagonal of the cuboid forms a right triangle with the height and the side of the square base.
Let's denote the height of the cuboid as "h". We also know that the side of the square base is 4 cm.
According to the Pythagorean theorem, the square of the length of the diagonal is equal to the sum of the squares of the other two sides:
diagonal^2 = height^2 + base^2
Plugging in the given values:
9^2 = h^2 + 4^2
81 = h^2 + 16
Rearranging the equation:
h^2 = 81 - 16
h^2 = 65
Taking the square root of both sides:
h = √65
Therefore, the height of the cuboid is approximately 8.06 cm.
To find the height of the cuboid, we will use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 lengths of the other two sides.
In this case, the diagonal of the cuboid forms the hypotenuse of a right triangle with the height of the cuboid and one side of the square base as the other two sides.
Let's denote the height of the cuboid as h. The length of the diagonal is given as 9 cm, and the side of the square base is 4 cm.
Using the Pythagorean theorem, we can write the equation as follows:
h^2 + 4^2 = 9^2
Simplifying this equation, we get:
h^2 + 16 = 81
Subtracting 16 from both sides, we have:
h^2 = 81 - 16
h^2 = 65
To find the height, we can take the square root of both sides:
h = √65
Therefore, the height of the cuboid is approximately equal to √65 cm.