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The volume of a cylinder is given by the formula V = 3.14rh, where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x+8) and height (2x+3). Which expression represents the volume of the can?

O (pi)x^3 + 19(pi)x^2 + 112(pi)x + 192(pi)

O 2(pi)x^3 + 35(pi)x^2 + 80(pi)x + 48(pi)

O 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

O 4(pi)x^3 + 44(pi)x^2 + 105(pi)x + 72(pi)

Respuesta :

The expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

The most fundamental of curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. From a geometric perspective, it may be compared to a prism with a circle as its basis.

Given the volume of a cylinder is given by the formula V = 3.14r^2h, where r is the radius of the cylinder and h is the height and suppose a cylindrical cane has radius (x+8) and height (2x+3)

We have to find expression which represents the volume of the cane

So as per given,

r = x+8

h = 2x + 3

v = πr²h

v = π(x+8)²(2x+3)

v = π(x²+64+16x)(2x+3)

v = π(2x³+128x+32x²+3x²+192+48x)

v = π(2x³+35x²+176x+192)

v = π2x³+π35x²+π176x+π192

Hence the expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)

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