9514 1404 393
Answer:
27.1 cm
Step-by-step explanation:
The area of the solid is the lateral area of the cylinder plus the total area of the cone of unknown height. In terms of the cone's slant height (s), the total area of the solid is ...
A = πdh +πr(r +s) . . . . diameter d, height h, radius r, slant height s
458 = π(6·18 +3(3+s))
145.786 = (108 +9 +3s)
28.786 = 3s
s = 9.595
Then the height of the cone is found from the Pythagorean theorem as ...
√(s² -3²) ≈ 9.1 . . . . cm
The total height of the solid is about ...
18 cm +9.1 cm = 27.1 cm
