A-Level Maths mock paper help

Can anyone explain to me whats going on with question 13?
I've looked at the MS too but still don't really get it, especially where the first line of the MS comes from...
Paper: https://hgsmaths.com/year-13/maths/past-papers/documents/mock-set-2/paper-1-qp.pdf
MS: https://hgsmaths.com/year-13/maths/past-papers/documents/mock-set-2/paper-1-ms.pdf

Reply 1

Darkwings_Lok

9

I think it is using ratios, which the ratio of radius and height is always the same, when the height decrease, the radius decrease in same ratio. So he can use the ratio to find r in first line and substitute it to the volume equation and differentiate to get dV/dh
r/h=2.5/4 so r=5/8h/
the dV/dh of the ans is 75/192 is not yet simplified

Reply 2

m184

13

Original post by h6yates

Can anyone explain to me whats going on with question 13?
I've looked at the MS too but still don't really get it, especially where the first line of the MS comes from...
Paper: https://hgsmaths.com/year-13/maths/past-papers/documents/mock-set-2/paper-1-qp.pdf
MS: https://hgsmaths.com/year-13/maths/past-papers/documents/mock-set-2/paper-1-ms.pdf

since both the radius and the height are unknown they formed a ratio of r and h to the height and radius of the water inside the cone (which is possible since the dimensions of the cone are proportionate throughout). that way, they can substitute r in the equation for the volume of the cone and replace it with h, this allows you to differentiate V with respect to h

Reply 3

Muttley79

20

Original post by h6yates

Can anyone explain to me whats going on with question 13?
I've looked at the MS too but still don't really get it, especially where the first line of the MS comes from...
Paper: https://hgsmaths.com/year-13/maths/past-papers/documents/mock-set-2/paper-1-qp.pdf
MS: https://hgsmaths.com/year-13/maths/past-papers/documents/mock-set-2/paper-1-ms.pdf

This is a standard approach - we have a formula for volume of a cone however this includes two variables - we need one variable to differentiate.

They are using similar triangles to get a formula connecting h and r to substitute.

Reply 4

leoishush

15

Original post by Muttley79

This is a standard approach - we have a formula for volume of a cone however this includes two variables - we need one variable to differentiate.

They are using similar triangles to get a formula connecting h and r to substitute.