Question

A block of ice in the form of a cube with sides x cm,melts at a rate of 9.72cm^3 per minute.Find the rate of change of x at the instant when x=12cm. Just to double check my working
@ganeshie8

Answer 1

This is my working..\[volume~of~a~cube,V=x^3\]\[\frac{ dv }{ dx }=3x^2\]\[\frac{ dv }{ dt }=\frac{ dv }{ dx }\times \frac{ dx }{ dt }\]\[-9.72=3x^2\times \frac{ dx }{ dt }\]\[\frac{ dx }{ dt }=\frac{ -9.72 }{ 3x^2 }\]\[\frac{ dx }{ dt }=\frac{ -9.72 }{ 3(12)^2 }\]\[\frac{ dx }{ dt }=-0.0225cm~s^{-1}\]

Answer 2

Looks perfect!

Answer 3

Thank you @ganeshie8 ^_^

Answer 4

great job

Answer 5

Thanks @triciaal :)

Answer 6

np, good job :)