Question

A solid has a circular base of radius 3. If every plane cross-section perpendicular to the x-axis is an equilateral triangle, then its volume is:
A) 36
B) 12sqrt3
C) 18sqrt3
D) 36sqrt3

Please try to explain as much as you can, I am very confused.

Answer 1

 An equilateral triangle has an Area = (1/2) a^2 sqrt3 
The base has an equation x^2+y^2 =9 

So at x , y= sqrt (9-x^2) 
The side of the triangle is a= 2y 
So dVolume = (1/2)a^2 sqrt3 dx 

dV= (sqrt 3) (9-x^2) dx 

V= sqrt3 INT (9-x^2) dx 
-3<x<3 
by simmetry , 

V= 2sqrt3 INT (9-x^2) dx 
0<x<3 

V= 2sqrt3 ( 9x-x^3/3) 

V= 2sqrt3 ( 27-9) 
V= 36 sqrt3 ANSWER 

Hope This Helped! :3

Answer 2

The volume should be option D) 36sqrt3

Calculation of the volume;

Since A solid has a circular base of a radius of 3.

The Area of the equilateral triangle should be

= $(1/2) \time a^2$

The equation of the base should be = $x^2+y^2 =9$

Now

at x ,

y= square root $(9-x^2)$

Side of the triangle  is a= 2y

Now the volume is

$V= 2\times ( 9x-x^3\div 3)\\\\V=2 \times ( 27-9)\\\\V= 2\times 18$

= 36sqrt3

hence, The volume should be option D) 36sqrt3

Learn more about triangles here: https://brainly.com/question/14663689