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
= 16+81
= 97
s = 9.8
Oh, calculating slant height, eh? Let me put on my "math clown" hat for this one! *ahem*
To find the slant height of a cone, we can use the Pythagorean Theorem, which 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 (the height and the radius).
So, let's get calculating! Since the diameter is 8cm, we can find the radius by dividing it by 2, giving us a radius of 4cm. Now we have a right-angled triangle with a height of 9cm and a base of 4cm.
Using the Pythagorean Theorem:
(hypotenuse)^2 = (height)^2 + (radius)^2
(slant height)^2 = 9^2 + 4^2
(slant height)^2 = 81 + 16
(slant height)^2 = 97
Now, let's find the square root to get the slant height:
slant height = √97 ≈ 9.8 cm
So, rounding to the nearest tenth, the slant height of the given cone is approximately 9.8 cm.
To calculate the slant height of the cone, we can use the Pythagorean theorem.
The radius of the cone can be found by dividing the diameter by 2: r = 8 cm / 2 = 4 cm.
Now, using the height and the radius, we can calculate the slant height (l) using the Pythagorean theorem: l = √(r^2 + h^2).
Substituting the values, we have: l = √(4 cm^2 + 9 cm^2).
Calculating this, we find: l ≈ √(16 cm^2 + 81 cm^2) ≈ √(97 cm^2) ≈ 9.8 cm.
Therefore, the slant height of the cone rounded to the nearest tenth is 9.8 cm.
To calculate the slant height of a cone, we can use the Pythagorean theorem. The slant height, labeled as "l", is the hypotenuse of a right triangle formed by the height of the cone (labeled as "h") and the radius of the cone (labeled as "r"). In this case, the diameter is given as 8 cm, so the radius is half of the diameter, which is 4 cm.
Using the Pythagorean theorem, we have:
l^2 = h^2 + r^2
Substituting the given values, we have:
l^2 = 9^2 + 4^2
l^2 = 81 + 16
l^2 = 97
To find the slant height, we take the square root of both sides:
l = √97
l ≈ 9.9 cm
Rounding to the nearest tenth, the slant height is approximately 10.2 cm.
Therefore, the correct answer is 10.2 cm.