# Maths Question

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#1
A factory which makes metal cubes contains a machine that heats cubes to strengthen them. When heated, the volume of the cube increases at a constant rate of 1.5cm^3s^-1

If the rate of increase of the total surface area of a cube is higher than 1 com^2s^-1 the cube will be damaged.

showing your working clearly, find the minimum side length that a cube must have so that it doesn't become damaged when heated

Any help will be appreciated as i have no idea where to start! thankyou
0
1 year ago
#2
(Original post by orangeorangutan)
A factory which makes metal cubes contains a machine that heats cubes to strengthen them. When heated, the volume of the cube increases at a constant rate of 1.5cm^3s^-1

If the rate of increase of the total surface area of a cube is higher than 1 com^2s^-1 the cube will be damaged.

showing your working clearly, find the minimum side length that a cube must have so that it doesn't become damaged when heated

Any help will be appreciated as i have no idea where to start! thankyou
It's a metal cube.

If we denote the side length as , then the volume is .

If you differentiate this eqn. with respect to time, what do you get?

The question clearly tells you that so use it. Rearrange the eqn. for . (*)

Now, what is the surface area of the cube in terms of ? Differentiate this eqn, and set the condition that . This gives a condition on if you rearrange for it.

Which means you can come back to the point (*) and apply that condition. Hence solve the inequality for .
Last edited by RDKGames; 1 year ago
0
1 year ago
#3
So would the answer be 6 or 9 because I got 9 but the book says 6?
(Original post by RDKGames)
It's a metal cube.

If we denote the side length as , then the volume is .

If you differentiate this eqn. with respect to time, what do you get?

The question clearly tells you that so use it. Rearrange the eqn. for . (*)

Now, what is the surface area of the cube in terms of ? Differentiate this eqn, and set the condition that . This gives a condition on if you rearrange for it.

Which means you can come back to the point (*) and apply that condition. Hence solve the inequality for .
0
1 year ago
#4
(Original post by kimmyanne123)
So would the answer be 6 or 9 because I got 9 but the book says 6?
It should be 6.
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