Volumes of Revolution (AQA A-Level Further Maths): Quizzes

📚Quizzes
Volumes of Revolution
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

What is the formula for volume when rotating y=f(x)y = f(x) about the x-axis from x=ax = a to x=bx = b?

V=∫abπy2 dxV = \int_a^b \pi y^2 \, dx

What is the formula for volume when rotating x=f(y)x = f(y) about the y-axis from y=ay = a to y=by = b?

V=∫abπx2 dyV = \int_a^b \pi x^2 \, dy

If rotating 360° gives volume VV, what volume results from rotating 180°?

12V\frac{1}{2}V

What does rotating through 2π radians mean?

A full 360° turn

When rotating about the x-axis, what must you square in the volume formula?

The yy value

Before rotating about the y-axis, what form must your equation be in?

x=f(y)x = f(y)

If you see dydy in a volume integral, which axis are you rotating about?

The y-axis

What is the formula for the volume of a cone?

V=13πr2hV = \frac{1}{3}\pi r^2 h

What is a common mistake when integrating (x3+1)2(x^3 + 1)^2?

Not expanding brackets before integrating

What is the first step in solving a volume of revolution problem?

Sketch the region

Join 100,000+ A-Level students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.