Question
Look at the cone below.
Height of the cone is 12 units and diameter is 8 units.
What is the slant height of the cone to the nearest tenth?
A.
16.0
B.
12.6
C.
11.3
D.
7.2
Height of the cone is 12 units and diameter is 8 units.
What is the slant height of the cone to the nearest tenth?
A.
16.0
B.
12.6
C.
11.3
D.
7.2
Answers
GPT 3.5
To find the slant height of the cone, we can use the Pythagorean theorem.
Since the height and radius of the cone are perpendicular, we can form a right triangle with the slant height as the hypotenuse, height as one leg, and the radius as the other leg.
Using the Pythagorean theorem, we have:
slant height^2 = height^2 + radius^2
slant height^2 = 12^2 + 4^2
slant height^2 = 144 + 16
slant height^2 = 160
Taking the square root of both sides, we get:
slant height = √160
slant height ≈ 12.65
Therefore, the slant height of the cone to the nearest tenth is 12.6 units.
Therefore, the answer is B. 12.6.
Since the height and radius of the cone are perpendicular, we can form a right triangle with the slant height as the hypotenuse, height as one leg, and the radius as the other leg.
Using the Pythagorean theorem, we have:
slant height^2 = height^2 + radius^2
slant height^2 = 12^2 + 4^2
slant height^2 = 144 + 16
slant height^2 = 160
Taking the square root of both sides, we get:
slant height = √160
slant height ≈ 12.65
Therefore, the slant height of the cone to the nearest tenth is 12.6 units.
Therefore, the answer is B. 12.6.