Rates of Change, SMB-004

Jacques is a marine biologist and finds that the mass of a crab `(M)` is directly proportional to the cube of the diameter of its shell `(d)`.

If a crab with a shell diameter of 15 cm weighs 680 grams, what will be the diameter of a crab that weighs 1.1 kilograms? Give your answer to 1 decimal place. (3 marks)

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`17.6\ text(cm)`

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`M`	`prop d^3`
`M`	`= kd^3`

`text(When)\ \ M=680, \ d=15`

`680`	`=k xx 15^3`
`k`	`=0.201481…`

`text(Find)\ \ d\ \ text(when)\ \ M=1100:`

`1100`	`=0.20148… xx d^3`
`d`	`=root3(1100/(0.20148…))`
	`=17.608…`
	`=17.6\ text{cm (to 1 d.p.)}`