Question

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If cylinder and the box have equal height, then what is the value of r in terms of x ?

Answer 1

Answer:

$r=\frac{1}{2\sqrt{\pi}}x$

Step-by-step explanation:

Base of rectangular box is square

So,Let  Base = Length = x

Let the height of box be h

Volume of box = $Length \times Breadth \times Height = x \times x \times h = x^2h$

Height of cylinder = Height of box = h

Radius of cylinder = r

Volume of cylinder = $\pi r^2 h$

We are given that The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box

So, $\pi r^2 h=\frac{1}{4} x^2h$

$\pi r^2=\frac{1}{4} x^2$

$r=\sqrt{\frac{1}{4 \pi} x^2}$

$r=\frac{1}{2\sqrt{\pi}}x$

Hence the value of r in terms of x is $r=\frac{1}{2\sqrt{\pi}}x$