To find the slant height of the cone, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
In this case, the diameter (d) of the cone is the base of a right triangle, and the height (h) of the cone is the other side of the triangle. The slant height (L) is the hypotenuse.
Using the Pythagorean Theorem: L^2 = d^2 + h^2
Given that the diameter (d) is 13 cm, and the height (h) is 6 cm, we can substitute these values into the equation:
L^2 = 13^2 + 6^2
L^2 = 169 + 36
L^2 = 205
To find L, we take the square root of both sides:
L = sqrt(205)
L ≈ 14.3 cm
Therefore, the slant height of the cone should be approximately 14.3 cm.
Use the image to answer the question.
A drawing shows a circle showing diameter below a sector of a circle showing slant height. A double-headed arrow crossing the center of the circle is labeled as d equals diameter. A dotted double-headed arrow is drawn from the top point of the sector of the circle to a point along the curved edge. The arrow is labeled as lower L equals slant height.
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
14.3 cm
14.3 cm
2.5 cm
2.5 cm
11.5 cm
11.5 cm
8.8 cm
1 answer