Calculate the slant height for the given cone. Round to the nearest tenth. Diameter = 18cm Height= 7cm
11.2 cm
12.5 cm
14.8 cm
11.4 cm
show work on how you got the answer :)
draw a side view. Note that if you drop an altitude to the center of the base of the cone, the slant height s is given by
s^2 = 9^2 + 7^2
radius at base = 18/2 = 9
height at center = 7
slant height = hypotenuse = sqrt (81+49)
To find 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 this case, the other two sides are the height and the radius of the base (half of the diameter).
First, let's find the radius:
Radius = Diameter / 2 = 18 cm / 2 = 9 cm
Next, let's find the square of the slant height:
Slant height squared = Height squared + Radius squared
Slant height squared = 7 cm squared + 9 cm squared
Slant height squared = 49 cm^2 + 81 cm^2
Slant height squared = 130 cm^2
Now, let's find the square root of 130 cm^2 to get the slant height:
Slant height = sqrt(130 cm^2) ≈ 11.4 cm
Therefore, the slant height of the given cone is approximately 11.4 cm. Hence, the correct option is 11.4 cm.
To calculate the slant height of a cone, you can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height and the radius (half the diameter).
First, we need to find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 18 cm / 2 = 9 cm
Now we can use the Pythagorean theorem to find the slant height. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we have:
Slant height^2 = Radius^2 + Height^2
Plugging in the values we know:
Slant height^2 = 9 cm^2 + 7 cm^2
Slant height^2 = 81 cm^2 + 49 cm^2
Slant height^2 = 130 cm^2
To find the slant height, we take the square root of both sides:
Slant height = √(130 cm^2)
Rounding this to the nearest tenth, we get:
Slant height ≈ √130 cm ≈ 11.4 cm
Therefore, the slant height of the given cone is approximately 11.4 cm.