Question

The volume of the solid formed when the
square ABCD is rotated about the line AB is 'k'.
What will be the volume of the solid formed
when the square is cut into half along the line
AC and again rotated about AB?
A k/2
D k/4
В.k/3
C k/9​

Answer 1

Answer:

HI BRO

Step-by-step explanatioNO

GJW

Answer 2

The volume of the figure thus formed is $\frac{1}{3}k$. (Option B)

Given,

A square ABCD rotated about side AB forms a solid with volume,

$V=k$

To find,

The volume of solid when side AC is halved and it is rotated again about side AB.

Solution,

The solid formed by rotating square ABCD along AB is a cylinder with

height of cylinder = radius of the cylinder

⇒$h=r=a$

So, we can say that

Height of cylinder, $h=AB=a$

The radius of the cylinder, $r=BC=a$

We know that,

The volume of the cylinder, $V= \pi r^{2}h$

⇒$V=\pi a^{2}a$

⇒$V=\pi a^{3}$

Now,

Rotating the square by its diagonal AC, we get a right circular cone with,

⇒$h'=BC=r$

And radius,

⇒$r'=AB=h$

Then, the new volume will be,

$V'=\frac{1}{3} \pi r'^{2}h'$

⇒$V'=\frac{1}{3}\pi r^{2}h$

⇒$V'=\frac{1}{3}\pi a^{3}$    

                ∵This is because $r=h=a$.

⇒$V'=\frac{1}{3}V$

⇒$V'=\frac{k}{3}$

Therefore, volume is decreased by one-third of the original volume. (Option B)