I think for these types of questions, actually graphing the functions out is useful to get a hang of the question. So, if you graph these functions, the region bounded would look like this:
As the question states that the cross sections taken perpendicular to the y-axis are squares, the area of the cross section (square) would be x^2.
As the formula for volume equals the integral of cross section area, the volume that this question asks can be written as following:
***Key informations***
Cross section area = x^2
f(x) = y = x^3 --> x = y^(1/3)
From y = 0 to y = 8
As we need to express the integrand in terms of y, we can rewrite the integral as following:
If you compute the above integral, we get a value of 19.2. Hence, the volume of the solid is 19.2
Hi,
Thank you for your question.
I think for these types of questions, actually graphing the functions out is useful to get a hang of the question. So, if you graph these functions, the region bounded would look like this:
As the question states that the cross sections taken perpendicular to the y-axis are squares, the area of the cross section (square) would be x^2.
As the formula for volume equals the integral of cross section area, the volume that this question asks can be written as following:
***Key informations***
Cross section area = x^2
f(x) = y = x^3 --> x = y^(1/3)
From y = 0 to y = 8
As we need to express the integrand in terms of y, we can rewrite the integral as following:
If you compute the above integral, we get a value of 19.2. Hence, the volume of the solid is 19.2
Does this answer your question?