A cone has a radius of 5cm and a height of 12cm. Calculate it's slant height
Cone has a base with diameter 6 cm and slant height 10 cm , calculate the height of the cone
To calculate the slant height of a cone, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In a cone, the slant height, radius, and height form a right triangle. The radius is one of the sides, and the height is the perpendicular side. Hence, we can write the equation as:
(slant height)^2 = (radius)^2 + (height)^2
Substituting the given values:
(slant height)^2 = (5cm)^2 + (12cm)^2
Calculating the right side of the equation:
(slant height)^2 = 25cm^2 + 144cm^2
(slant height)^2 = 169cm^2
Taking the square root of both sides to find the slant height:
slant height = √(169cm^2)
slant height ≈ √(169) cm
slant height ≈ 13 cm
The slant height of the cone is approximately 13 cm.
the radius , height , and slant height form a right triangle
... with the slant height as the hypotenuse
hint ... it's a Pythagorean triple