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3 May, 03:12

A hemispherical depression is cut out from one face of a cuboidal wooden block of edge 21cm such that the diameter of the hemisphere is equal to the edge of the cube. Determine the total surface area of the remaining block

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  1. 3 May, 03:30
    0
    (2646 + 110.25π) cm² ≈ 2992.4 cm²

    Step-by-step explanation:

    The area of a sphere is 4 times the area of a circle with the same radius. Hence the area of a hemisphere will be 2 times the area of that circle. This means carving a hemispherical depression in the face of the cube will add an area that is equal to the area of the circular hole.

    Of course the total surface area of a cube is 6 times the area of one square face. The area of a circle is ...

    A = πr² = π (d/2) ² = (π/4) d²

    The total surface area of the carved cube is ...

    S = 6· (21 cm) ² + (π/4) · (21 cm) ² = (441 cm²) (6 + π/4)

    S ≈ 2992.36 cm²

    The total surface area of the remaining block is about 2992.4 cm².
  2. 3 May, 03:32
    0
    (2646 + 110.25π) cm² ≈ 2992.4 cm²
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