The region, \(R\), bounded by the hyperbola \(y=\dfrac{60}{x+5}\), the line \(x=10\) and the coordinate axes is shown. Find the volume of the solid of revolution formed when the region \(R\) is rotated about the \(y\)-axis. Leave your answer in exact form. (4 marks) --- 8 WORK AREA LINES (style=lined) ---
Calculus, EXT1 C3 SM-Bank 3
Find the volume of the solid of revolution formed when the graph of `y = sqrt((1 + 2x)/(1 + x^2))` is rotated about the `x`-axis over the interval `[0,1]`. (3 marks)
Calculus, EXT1* C3 2017 HSC 12b
Calculus, EXT1* C3 2016 HSC 15a
The diagram shows two curves `C_1` and `C_2.` The curve `C_1` is the semicircle `x^2 + y^2 = 4, \ -2 <= x <= 0.` The curve `C_2` has equation `x^2/9 + y^2/4 = 1, \ 0 <= x <= 3.`
An egg is modelled by rotating the curves about the `x`-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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Calculus, EXT1* C3 2007 HSC 3a
Find the volume of the solid of revolution formed when the region bounded by the curve `y = 1/(sqrt(9 + x^2))`, the `x`-axis, the `y`-axis and the line `x = 3`, is rotated about the `x`-axis. (3 marks)
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Calculus, EXT1* C3 2015 HSC 16b
Calculus, EXT1* C3 2008 HSC 6c
The graph of `y = 5/(x - 2)` is shown below.
The shaded region in the diagram is bounded by the curve `y = 5/(x - 2)`, the `x`-axis and the lines `x = 3` and `x = 6`.
Find the volume of the solid of revolution formed when the shaded region is rotated about the `x`-axis. (3 marks)
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