Question

Consider the solid S described below.

The base of S is the triangular region wi

Answer 1

Consider the solid S described below.
The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the x-axis are equilateral triangles.
Find the volume V of this solid.

Answer 2

Are you kidding me? I appreciate you help but that is like asking me something in chinese.

Answer 3

haha :)

Answer 4

i dont get this question

Answer 5

it best to try to draw it out to get an idea of the visualization.
The base is a right triangle and if you cut it vertically each cross-section is a equilateral triangle.
volume is the infinite sum of all the cross-sectional areas

Answer 6

goal is to represent area of equilateral triangle in terms of x.
then integrate from 0 to 2 with respect to x

Answer 7

Area of equilateral triangle = \[\frac{\sqrt{3}}{4}s^{2}\]
where s is length of a side
s is represented by the length from the x-axis to the hypotenuse of base for each cross-section.
The line from (0,2) to (2,0) is
\[y = 2-x\]
so s = 2-x
As x gets bigger the cross-sectional areas get smaller
The integral should look like this:
\[V = \int\limits_{0}^{2}\frac{\sqrt{3}}{4}(2-x)^{2} dx\]

Answer 8

Are you serious? Thanks but I don't get it.

Answer 9

Finding volume of a solid is tough to teach online...you need a visual.
this is a calc 2 type problem
is this question for you dumbunny? or vaska?

Answer 10

so did that help?
can you do the integration from here?

Answer 11

yes, thanks...

Answer 12

ok your welcome
in general for these type of problems
\[V = \int\limits_{}^{}A(x) dx\]
where A is area of cross-section