The total air of the solid is 458 cm². What is the total height of the solid

9514 1404 393

  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

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step-by-step explanation:

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