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dedylja [7]
3 years ago
10

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

Mathematics
2 answers:
kolbaska11 [484]3 years ago
6 0

Answer:

Volume of cylinder = \pi r^2h

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 = \pi r^2

Area of square = s^2

Side of square = diameter of circle= D^2

Diameter = 2r

∴ Area of square=  2r^2=4r^2

\frac{Area of circle}{Area of Square}=\frac{\pi r^2}{4r^2}=\frac{\pi}{4}

Area of circle is \frac{\pi }{4}  of area of square.

Volume is always = area × height

Volume of prism = Area of square × h = 4r^2h

Volume of cylinder = Area of circle × h = \pi r^2h

Now, rate

\frac{Volume of cylinder}{Volume of prism}=\frac{\pi r^2h}{4r^2h}=\frac{\pi}{4}

⇒Volume of cylinder is  \frac{\pi }{4}  of Volume of prism.

Volume of Cylinder =\frac{\pi }{4}\times Volume of prism

Volume of cylinder = \frac{\pi }{4}\times 4r^2h

Volume of cylinder = \pi r^2h

Lana71 [14]3 years ago
4 0
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 
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