Calculate the slant height for the given cone. Round to the nearest tenth.
Diameter = 8cm
height = 9 cm
10.2 cm
11.4 cm
9.8 cm
12.0 cm****
s^2 = r^2 + h^2 = (d/2)^2 + h^2
s^2 = 4^2+9^2 = 16+81 = 97
s = 9.8
thank you for correcting me (: @steve
To calculate the slant height of a cone, you can use the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle, with the base being half the diameter (r) and the height (h) being the other side.
Given:
Diameter (d) = 8 cm
Height (h) = 9 cm
To find the radius (r), divide the diameter by 2:
r = d/2 = 8 cm / 2 = 4 cm
Now, we can calculate the slant height:
l = √(r^2 + h^2) = √(4^2 + 9^2) = √(16 + 81) = √97
Rounding to the nearest tenth, the slant height is approximately 9.8 cm.
Therefore, the correct answer is 9.8 cm (option C).
The slant height of a cone can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the case of a cone, the slant height is the hypotenuse, the height is one side, and the radius (half of the diameter) is the other side. The formula for the slant height is:
Slant height = √(height^2 + radius^2)
Given that the diameter is 8cm, the radius is half of that, which is 8/2 = 4cm. The height is given as 9cm.
Using the formula, we can calculate the slant height:
Slant height = √(9^2 + 4^2)
Slant height = √(81 + 16)
Slant height = √97
Slant height ≈ 9.8 cm
Therefore, the correct answer is 9.8 cm.