The diagram shows a cone of radius 5 cm and slant height 13 cm Calculate the perpendicular height h of the cone
Pythagorean Theorem:
In a triangle, side squared + side squared = hypotenuse squared
5^2 + h^2 = 13^2
Solve for h (height).
5^2 + h^2= 13^2
25+?=169=169-25=144.=12.
Am I correct?
To calculate the perpendicular height (h) of the cone, we can 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 slant height of the cone (13 cm) is the hypotenuse, and the radius of the cone (5 cm) is one of the other two sides. Let's call the perpendicular height h, which is the missing side of the right triangle.
Using the Pythagorean Theorem, we can write the equation:
h^2 + 5^2 = 13^2
Simplifying the equation:
h^2 + 25 = 169
Subtracting 25 from both sides:
h^2 = 144
Taking the square root of both sides:
h = √144
Simplifying the square root:
h = 12 cm
Therefore, the perpendicular height (h) of the cone is 12 cm.