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The radius of a cylinder was 3 centimeters, while the height of the cylinder was 10 centimeters, but both the radius and the height have begun increasing with time. The radius of the cylinder in centimeters can be defined by the function r(t) = 3+t, where t is the time elapsed in minutes, while the height of the cylinder in centimeters can be defined by the function h(t) = 10+t. Which of these functions represents the volume of the cylinder in cubic centimeters?

v(t) = πt^2+13πt + 30π

v(t) = t^3+16t^2+69t+90

v(t) = πt^3+16πt^2+96πt + 90π

v(t) = t^2+13t+30

Julius  Jan 18, 2018

#1
+6250
+2

volume of cylinder   =   π (radius)2 (height)

radius of the cylinder  =  3 + t      and      height of the cylinder  =  10 + t      so...

volume of cylinder   =   π (3 + t)2 (10 + t)

volume of cylinder   =   π (3 + t)(3 + t)(10 + t)

volume of cylinder   =   π ( t3 + 16t2 + 69t + 90 )

volume of cylinder   =   πt3 + 16πt2 + 69πt + 90π

hectictar  Jan 18, 2018
Sort:

#1
+6250
+2

volume of cylinder   =   π (radius)2 (height)

radius of the cylinder  =  3 + t      and      height of the cylinder  =  10 + t      so...

volume of cylinder   =   π (3 + t)2 (10 + t)

volume of cylinder   =   π (3 + t)(3 + t)(10 + t)

volume of cylinder   =   π ( t3 + 16t2 + 69t + 90 )

volume of cylinder   =   πt3 + 16πt2 + 69πt + 90π

hectictar  Jan 18, 2018

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