The diagram shows a gizmo where a cylinder is connected to a hemisphere with the same radius. The gizmo is held vertical by a thin straight rod which is connected to a horizontal plate and the top rim of the cylinder. The total volume of the gizmo is 9.8cm cubed. The radius of the hemisphere and cylinder is 0.8cm. Calculate the length of the rod.

extra info: The angle between the plate and the rod is 72°

Question

Roger Anthony

Mathematics

15 January, 03:57

The diagram shows a gizmo where a cylinder is connected to a hemisphere with the same radius. The gizmo is held vertical by a thin straight rod which is connected to a horizontal plate and the top rim of the cylinder. The total volume of the gizmo is 9.8cm cubed. The radius of the hemisphere and cylinder is 0.8cm. Calculate the length of the rod.

extra info: The angle between the plate and the rod is 72°

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Answers (1)

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Gabriel Mitchell · Answer 1

5.1cm

Step-by-step explanation:

volume of hemisphere = 1.07cm³

9.2-1.07 = 8.13

volume of cylinders = 8.13cm³

height of cylinder = 4.04cm

total height of gizmo = 4.04+0.8=4.84

4.84/sin (72) = 5.1cm