Final answer:
To find the radius of the base of the Pyraminx, we start by applying the Pythagorean theorem to the equilateral triangle that composes the faces. We can then calculate the radius as half of the height of this triangle. The correct radius is approximately 4.4 cm to the nearest tenth, not matching any of the provided options.
The correct answer is none of all.
Step-by-step explanation:
To solve for the radius (r) of the base of a Pyraminx (a tetrahedron), we need to consider the properties of an equilateral triangle, since the Pyraminx is composed of such triangles. Given the edge length is 15 cm and the height (h) of the pyramid is 12.2 cm, and knowing that the triangle with dashed lines is a right triangle, we can use the Pythagorean theorem to solve for the radius. The radius, in this case, will be half the length of the side of the triangle since the inscribed circle of an equilateral triangle touches the midpoint of each side.
Using the Pythagorean theorem, for an equilateral triangle:
A² + B² = C²
(h²) + (r²) = (15²)
(12.2²) + (r²) = 225
(148.84) + (r²) = 225
(r²) = 76.16
r = √76.16
r ≈ 8.7 cm
However, since we need to provide the radius of the base which is half the height of the equilateral triangle, we divide this number by 2 to get:
r = 8.7 cm / 2
r ≈ 4.4 cm
So the correct answer is none of the options provided is correct. The radius of the base of the pyramid is approximately 4.4 cm, to the nearest tenth of a centimeter.