C2 Question

A cyclindrical biscuit tin has a close-fitting lid which overlaps the tin by 1cm. The radii of the tin and the lid are both x cm. The tin and the lid are made from a thin sheet of metal of area 80pi cm^2 and there is no wastage. The volume of the tin is V cm^3

Show that V- pi(40x - x^2 - x^3)

Any tips or help is very much appreciated. Thank you in advance :-)

Reply 1

Chewwy

17

ah man, this is gonna take a while to type up.

so... pseudomath:

80pi = ((volume x circumference)/bottom area) + (2xbottom area) + (circumference x 1)

make the bit with volume in subject

cancel pi

multiply by denominator

divide by 2x

factorise.

voila.

Reply 2

Aitch

2

Tut

A cyclindrical biscuit tin has a close-fitting lid which overlaps the tin by 1cm. The radii of the tin and the lid are both x cm. The tin and the lid are made from a thin sheet of metal of area 80pi cm^2 and there is no wastage. The volume of the tin is V cm^3

Show that V- pi(40x - x^2 - x^3)

Any tips or help is very much appreciated. Thank you in advance :-)

You need some numbers:

Lid + bottom: 2pix²
lid overlap:2pix
side: 2pixh

area of sheet used:
2pix² + 2pix + 2pixh = 80pi

Get the height h

...

get h = (40 - x²)/x - 1

use this h value to calc V

V = pi x² h = pi x²[(40 - x²)/x - 1]

...

get V = pi[40x - x² -x³]

as req.

Aitch

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