Volume of a Solid

[meowmix]

Hi everyone, I have a problem I would like some help with. I don't really know where to start; it would be much appreciated if people could support me in figuring this one out.

The problem is as follows:

Let "R" be the region bounded by the x-axis,
the graph of y = sqroot x
and the line x = 4

Vertical line x = k divides region R into two regions such that when these two regions are revolved about the x-axis, they generate solids with equal volumes.
Find the value of k.

 

[Deleted member 4993]

Hi everyone, I have a problem I would like some help with. I don't really know where to start; it would be much appreciated if people could support me in figuring this one out.

The problem is as follows:

Let "R" be the region bounded by the x-axis,
the graph of y = sqroot x
and the line x = 4

Vertical line x = k divides region R into two regions such that when these two regions are revolved about the x-axis, they generate solids with equal volumes.
Find the value of k.

Start with sketching the region - and finding the limits of integrations.

 

[HallsofIvy]

Do you know how to find a "volume of revolution"? If so find the volume given by this figure from x= 0 to x= k (as a function of k), find the volume given by the figure from x= k to x= 4, set them equal and solve for k.