A company produces custom-made storage containers. One design consists of a cylinder attached to a hemisphere. The provided diagram [VISUALIZATION: A diagram showing a cylinder of radius (r) and height (h) standing vertically. A hemisphere with the same radius (r) is attached to the top circular face of the cylinder, forming a lid.] illustrates the configuration. The cylinder has a radius (r) cm and height (h) cm, and the hemisphere has the same radius (r) cm. The total height of the container is 35 cm. The radius (r) is 10 cm.
(a) Calculate the height (h) of the cylinder. \[2\]
(b) Calculate the volume of the container. \[4\]
(c) Calculate the total surface area of the container (including the base). \[5\]
Point A is on the circumference of the base of the cylinder. Point B is the highest point on the hemisphere (the pole). Point C is the centre of the base of the cylinder.
(d) Calculate the angle of elevation of B from A. \[4\]
Part a
2 minutes
2 marks
Question
Calculate the height (h) of the cylinder. \[2\]
Hint Hint
Hint
Subtract the hemisphere’s height (which equals the radius, 10 cm) from the total height (35 cm).
Answer Answer
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Answer Answer
Complete Answer
h = 25 cm
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Part b
4 minutes
4 marks
Question
Calculate the volume of the container. \[4\]
Hint Hint
Hint
Calculate the volumes of the cylinder and hemisphere separately then add them.
Answer Answer
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Answer Answer
Complete Answer
Volume = (9500/3)π cm³
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Part c
5 minutes
5 marks
Question
Calculate the total surface area of the container (including the base). \[5\]
Hint Hint
Hint
Add the curved surface area of the hemisphere, the lateral surface area of the cylinder, and the area of the base.
Answer Answer
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Answer Answer
Complete Answer
Surface area = 800π cm²
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Part d
4 minutes
4 marks
Question
Calculate the angle of elevation of B from A. \[4\]
Hint Hint
Hint
Use the triangle formed by A, B, and C, where AC = 10 cm and BC = 35 cm (as indicated in the diagram). Apply the tangent function.
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