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"The diameter and height of this cylinder are equal to the side length, S, of the cube in which the cylinder is inscribed. What is the expression for the cylinder's volume?
a) V=1/4piS^3
b) V=1/3piS^2
c) V=1/13piS^3
d) V=piS^2"

The diameter and height of this cylinder are equal to the side length S of the cube in which the cylinder is inscribed What is the expression for the cylinders class=

Respuesta :

HomertheGenius
Volume of a cylinder:
V = r² π h
r = S/2,  h = S
V = ( S/2 )² · π · S  = S²/4 · π · S = 1/4 π S³ 
Answer: A )

[tex]\rm V=\frac{1}{4}\pi S^3[/tex], is the expression for the cylinder's volume. Option A is correct.

What is the definition of a cylinder?

A cylinder is a closed solid with two parallel circular bases and a curving surface connecting them.

Given data;

Diameter(d)

Height(h)

side length cube (S)

Volume of the cylinder(V)

Given condition'

d=h=S

r = S/2

The volume of a cylinder is found as;

[tex]\rm V = \pi r^2 h \\\\ V = \pi (\frac{S}{2} )^2 \\\\ V== \pi \frac{S^2}{4}S \\\\ V =\frac{1}{4} \pi S^3[/tex]

[tex]\rm V=\frac{1}{4}\pi S^3[/tex], is the expression for the cylinder's volume.

Hence option A is correct.

To learn more about the cylinder, refer;

https://brainly.com/question/3692256.

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