A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or nr^2 or n/4. Since the area of the circle is n/4 the area of the square, the volume of the cylinder equals

This is the concept of ratios and proportionality;
The area of the circle is π/4, the linear scale factor will be given by:
sqrt(π/4)
=(sqrt π)/2
Therefore the volume will be given by:
(Area scale factor)^3
=[(sqrt π)/2]^3
=(π^(3/2))/8

Answer Link

tardymanchester tardymanchester · Answer 2 · 2019-01-08T07:36:15+01:00

Answer:

Volume of cylinder = [tex]\pi r^2h[/tex]

Step-by-step explanation:

Given : A cylinder fits inside a square prism.

To find : The volume of cylinder

Solution : Refer the attached graph.

Area of circle = [tex]\pi r^2[/tex]

Area of square = [tex]s^2[/tex]

Side of square = diameter of circle= [tex]D^2[/tex]

Diameter = 2r

∴ Area of square= [tex]2r^2=4r^2[/tex]

[tex]\frac{Area of circle}{Area of Square}=\frac{\pi r^2}{4r^2}=\frac{\pi}{4}[/tex]

Area of circle is [tex]\frac{\pi }{4}[/tex] of area of square.

Volume is always = area × height

Volume of prism = Area of square × h = [tex]4r^2h[/tex]

Volume of cylinder = Area of circle × h = [tex]\pi r^2h[/tex]

Now, rate

[tex]\frac{Volume of cylinder}{Volume of prism}=\frac{\pi r^2h}{4r^2h}=\frac{\pi}{4}[/tex]

⇒Volume of cylinder is [tex]\frac{\pi }{4}[/tex] of Volume of prism.

Volume of Cylinder =[tex]\frac{\pi }{4}\times Volume of prism [/tex]

Volume of cylinder = [tex]\frac{\pi }{4}\times 4r^2h [/tex]

Volume of cylinder = [tex]\pi r^2h[/tex]