Cylinder's Volume

Geometry Level 2

A rectangle of length b b and width a a is rolled about its length. The volume of the resulting cylinder is:

π a 2 b \pi a^{2}b b 2 a 4 π \frac{b^{2}a}{4\pi} 2 π a b 2\pi ab a 2 b 4 π \frac{a^{2}b}{4\pi}

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Most will see the figure and conclude that a a is the radius. The question clearly states that the rectangle has been rolled about b b to form the cylinder.

So height, H H of the cylinder = b b

But radius, R R of the cylinder is related as follows: a = 2 π R a = 2\pi R ⟹ \implies R R = a 2 π \frac{a}{2\pi}

We know that volume of a cylinder = π R 2 H \pi R^{2}H = π a 2 b 4 π 2 \frac{\pi a^{2}b}{4 \pi^{2}} = a 2 b 4 π \frac{a^{2}b}{4\pi}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...