A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm . Find the inner surface area and the volume of the vessel. 30/1/3 This section consists of 5 questions of 2 marks each.
Explanation
The inner surface area of the vessel is the sum of the curved surface area of the hemisphere and the curved surface area of the cylinder. The curved surface area of the hemisphere is 2πr² and the curved surface area of the cylinder is 2πrh. The total inner surface area is 2πr² + 2πrh. The volume of the vessel is (1/2)πr³ + πr²h. Given that the diameter of the hemisphere is 14 cm, the radius is 7 cm. The total height of the vessel is 13 cm, so the height of the cylinder is 6 cm. Substituting these values, we get the inner surface area as 2π(7)² + 2π(7)(6) = 98π + 84π = 182π and the volume as (1/2)π(7)³ + π(7)²(6) = 171.75π + 294π = 465.75π.
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