orangeorangutan
Badges: 9
Rep:
?
#1
Report Thread starter 1 year ago
#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
reply
RDKGames
Badges: 20
Rep:
?
#2
Report 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 x, then the volume is V = x^3.

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

The question clearly tells you that \dfrac{dV}{dt} = 1.5 so use it. Rearrange the eqn. for x\dfrac{dx}{dt}. (*)


Now, what is the surface area S of the cube in terms of x? Differentiate this eqn, and set the condition that \dfrac{dS}{dt} \leq 1. This gives a condition on x\dfrac{dx}{dt} if you rearrange for it.

Which means you can come back to the point (*) and apply that condition. Hence solve the inequality for x.
Last edited by RDKGames; 1 year ago
0
reply
kimmyanne123
Badges: 7
Rep:
?
#3
Report 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 x, then the volume is V = x^3.

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

The question clearly tells you that \dfrac{dV}{dt} = 1.5 so use it. Rearrange the eqn. for x\dfrac{dx}{dt}. (*)


Now, what is the surface area S of the cube in terms of x? Differentiate this eqn, and set the condition that \dfrac{dS}{dt} \leq 1. This gives a condition on x\dfrac{dx}{dt} if you rearrange for it.

Which means you can come back to the point (*) and apply that condition. Hence solve the inequality for x.
0
reply
RDKGames
Badges: 20
Rep:
?
#4
Report 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.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (95)
13.83%
I'm not sure (32)
4.66%
No, I'm going to stick it out for now (215)
31.3%
I have already dropped out (16)
2.33%
I'm not a current university student (329)
47.89%

Watched Threads

View All
Latest
My Feed