mikaloveskero said:Homework Statement
The area bounded by y=√x, the x-axis and the line x=9 and is perpendicular to the x axis. find the volume of the cross section using rectangle with the h=1/2b
Homework Equations
The Attempt at a Solution
I just want to know if I'm correct or on the right track. if not please correct me
A=HB
A=(1/2B)B =3/2B
So i take the integral of 3/2B from 0 to 9
V=3/2 integral 0 to 9 B
V=3B^2/4 from 0 to 9
V=243/4
LCKurtz said:You haven't stated the problem clearly enough to be sure what it actually is, but I'm pretty certain your solution is wrong anyway.
Does the solid you are trying to describe sit on the described area with rectangular cross-sections perpendicular to the xy plane? Are the bases of the rectangular cross-sections in the xy plane perpendicular to the x-axis?
mikaloveskero said:Yes, it does sit on the area with rectangular cross sections perpendicular to the x and y plane and the bases of the rectangular cross section are perpendicular to the x axis. I just need to find the volume using the given information.
Also i realize an error in my work :
A=HB
A=(1/2B)B =3/2√ x
So i take the integral of 3/2√x from 0 to 9
V=3/2 integral 0 to 9 x^3/2/(3/2)
V=6x^3/2/(6) from 0 to 9
V=162/6
or
The base is going to be sqrt(x). Therefore the height is 1/2sqrt(x), and the area is 1/2 x. The volume will be the integral from 0 to 9 of 1/2 x, which is 81/4.
i get two different answers
The concept of volume of cross sections using rectangles is a mathematical method used to find the volume of a three-dimensional shape by calculating the area of its cross sections made up of rectangles.
Calculating the volume of cross sections using rectangles is important because it allows us to find the volume of irregularly shaped objects, such as cylinders, cones, and pyramids, which cannot be easily measured using traditional methods.
The steps to calculate the volume of cross sections using rectangles are:
The concept of volume of cross sections using rectangles has various real-life applications, such as in architecture and engineering to design and construct buildings and bridges, in manufacturing to create and measure objects, and in medicine to calculate the volume of organs and tumors.
Some common mistakes to avoid when calculating the volume of cross sections using rectangles include: