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
8.8 cm
8.8 cm
11.5 cm
11.5 cm
2.5 cm
To find the slant height of the cone, we can use the Pythagorean theorem to solve for the missing side. The equation for the Pythagorean theorem is a^2 + b^2 = c^2, where c is the hypotenuse (slant height) and a and b are the other two sides (radius and height).
In this case, the diameter of the circle (2r) is 13 cm, so the radius (r) is 13/2 = 6.5 cm. The height of the cone (b) is given as 6 cm.
Applying the Pythagorean theorem:
6.5^2 + 6^2 = c^2
42.25 + 36 = c^2
78.25 = c^2
c ≈ √78.25
c ≈ 8.8 cm
Therefore, the slant height of the cone must be approximately 8.8 cm.