Using algebraic integration, find the exact volume of the solid of revolution formed when the region $R\,$ is rotated through $2\pi\,$ radians about the $x$ -axis.

[7]

1.5.16 Gradient of a parametric curve (A-level only) Questions

A Level
Maths
1.5.16 Gradient of a parametric curve (A-level only)

A Level
Maths OCR (MEI)
Question bank

1.5.16 Gradient of a parametric curve (A-level only)

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Question 5

A curved profile for a glass sculpture $C\,$ is modeled by the parametric equations

\frac{1}{4}t^2 + 1, \quad y = 2t - \frac{8}{t}, \quad t > 0

The curve $C\,$ intersects the $x$ -axis at the point $Q$ .

Find the $x$ -coordinate of $Q$ .

[1]

The line $l\,$ is the normal to $C\,$ at the point $P$ . Given that $t = 4$ at $P$ :

Write down the coordinates of $P$ .

[2]

Using calculus, show that an equation of $l\,$ is

4 x + 5 y = 50

[4]

The region $R\,$ is bounded by the curve $C$ , the line $l$ , and the $x$ -axis.

Using algebraic integration, find the exact volume of the solid of revolution formed when the region $R\,$ is rotated through $2\pi\,$ radians about the $x$ -axis.

[7]

1.5.16 Gradient of a parametric curve (A-level only) Questions

A Level
Maths
1.5.16 Gradient of a parametric curve (A-level only)