Respuesta :

Radius = Diameter ÷ 2

Radius = 9 ÷ 2 = 4.5 cm

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Volume of the semi-circle prism = 1/2 πr² h

Volume = 1/2 π (4.5)² (42) = 1336 cm³

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Volume of he rectangle prism = L x W x H

Volume = 42 x 35 x 9 = 13230 cm³

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Total volume = 1336 + 13230 = 14566 cm³

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Answer: 14566 cm³

It would be easier if we split the composite solid into a rectangular prism and a half of a cylinder.

The volume of the prism is easy: length * width * height: 35 * 9 * 42 = 13230 cm cubed.

The half of the cylinder is just: (pi * r^2 * h)/2

The diameter is 9, so the radius is 4.5. The height is 42. So:

(pi * 4.5^2 * 42)/2 is about 1335.96

1335.96 + 13230 = 14565.96 or, rounding up, 14566 cm cubed.