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Calculus, EXT1 C3 2023 HSC 12e

The region, , bounded by the hyperbola , the line and the coordinate axes is shown.

Find the volume of the solid of revolution formed when the region is rotated about the -axis. Leave your answer in exact form. (4 marks)

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♦ Mean mark 49%.

Calculus, EXT1 C3 SM-Bank 3

Find the volume of the solid of revolution formed when the graph of is rotated about the -axis over the interval . (3 marks)

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Calculus, EXT1* C3 2017 HSC 12b

The diagram shows the region bounded by and the -axis.

The region is rotated about the -axis to form a solid.

Find the exact volume of the solid formed. (3 marks)

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Calculus, EXT1* C3 2016 HSC 15a

The diagram shows two curves and The curve is the semicircle The curve has equation

An egg is modelled by rotating the curves about the -axis to form a solid of revolution.

Find the exact value of the volume of the solid of revolution. (4 marks)

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$³$

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	$³$

Calculus, EXT1* C3 2007 HSC 3a

Find the volume of the solid of revolution formed when the region bounded by the curve , the -axis, the -axis and the line , is rotated about the -axis. (3 marks)

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$³$

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	$³$

Calculus, EXT1* C3 2015 HSC 16b

A bowl is formed by rotating the curve about the -axis for

Find the volume of the bowl. Give your answer correct to 1 decimal place. (3 marks)

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$³$

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♦ Mean mark 38%.

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Calculus, EXT1* C3 2008 HSC 6c

The graph of is shown below.

The shaded region in the diagram is bounded by the curve , the -axis and the lines and .

Find the volume of the solid of revolution formed when the shaded region is rotated about the -axis. (3 marks)

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$³$

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	$³$

Calculus, EXT1* C3 2014 HSC 14c

The region bounded by the curve and the -axis between and is rotated about the -axis to form a solid.

Find the volume of the solid. (3 marks)

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$³$

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	$³$

Calculus, EXT1* C3 2012 HSC 14b

The diagram shows the region bounded by , the -axis, the -axis, and the line .

The region is rotated about the -axis to form a solid.

Find the volume of the solid. (3 marks)

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$³$

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MARKER’S COMMENT: Most students omitted the

when stating the definite integral in this question!









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