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`

Volume = πr²h

Diameter = S

Height = S

Radius = S/2

Volume = π ( s²/4 ) s

1/4 πs³

The required answer is in the option ( A )

Hope helps!

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.