find the height of the cone whose land height is thirty four centimeter and base diameter is thirty two centimeter
To find the height of the cone, we can use the Pythagorean theorem.
The land height is given as 34 centimeters, which is the perpendicular distance from the base to the apex. The base diameter is given as 32 centimeters, which is the length of the base across the widest part.
Let's assume the radius of the base is denoted by r. Since the diameter is 32 centimeters, the radius is half of that, i.e., r = 32/2 = 16 centimeters.
Now, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the radius r is one side, the height h (which we want to find) is the other side, and the land height 34 centimeters acts as the hypotenuse.
Using the Pythagorean theorem, we have:
h^2 + r^2 = land height^2
h^2 + 16^2 = 34^2
h^2 + 256 = 1156
h^2 = 1156 - 256
h^2 = 900
Taking the square root of both sides, we get:
h = √900
h = 30 centimeters
Therefore, the height of the cone is 30 centimeters.