The Pythagorean Theorem in Three Dimensions Quick Check 3 of 53 of 5 Items Question Use the image to answer the question. Chem Tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth. (1 point) Responses 2.5 cm 2.5 cm 14.3 cm 14.3 cm 8.8 cm 8.8 cm 11.5 cm
To find the slant height of the cone, we can use the Pythagorean Theorem which states that in a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
Given:
Height = 6 cm
Diameter = 13 cm (radius = 6.5 cm)
Using Pythagorean Theorem:
hypotenuse^2 = height^2 + radius^2
hypotenuse^2 = 6^2 + 6.5^2
hypotenuse^2 = 36 + 42.25
hypotenuse^2 = 78.25
hypotenuse ≈ √78.25
hypotenuse ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm.
The correct answer is:
8.8 cm