Volumes of Revolution (Edexcel A-Level Further Mathematics): Quizzes

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Modelling with Volumes of Revolution
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What is integrated to find a volume of revolution?

The squared radius times π\pi

Which formula gives volume when rotating about the xx-axis?

V=πab[y(x)]2dxV = \pi \int_a^b [y(x)]^2 \, dx

Which formula gives volume when rotating about the yy-axis?

V=πab[x(y)]2dyV = \pi \int_a^b [x(y)]^2 \, dy

What is the volume of y=x2y = x^2 from x=0x=0 to x=2x=2 rotated about the xx-axis?

32π5\frac{32\pi}{5}

What is the volume of x=yx = \sqrt{y} from y=1y=1 to y=4y=4 rotated about the yy-axis?

15π2\frac{15\pi}{2}

A hollow pipe has outer radius 3, inner radius 2, length 10. What is its volume?

50π50\pi

What common mistake involves the radius in volume of revolution formulas?

Forgetting to square it

For rotation about the xx-axis, which limits should be used?

xx-limits

What is the formula for the volume of a cylinder?

V=πr2hV = \pi r^2 h

How do you find the volume of a composite solid like a hollow pipe?

Subtract inner volume from outer

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