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Math c2 help i have exam tmw

a solid wooden block. The block is a right prism with length hcm. The
cross-section of the block is a semi-circle with radius rcm.
The total surface area of the block, including the curved surface, the two semi-circular
ends and the rectangular base, is 200cm2
(a) Show that the volume Vcm3 of the block is given by
V=πr(200-πr^2)/4+2π
(b) Use calculus to find the maximum value of V. Give your answer to the nearest cm3.

(c) Justify, by further differentiation, that the value of V that you have found is a
maximum.
Original post by sarah5
a solid wooden block. The block is a right prism with length hcm. The
cross-section of the block is a semi-circle with radius rcm.
The total surface area of the block, including the curved surface, the two semi-circular
ends and the rectangular base, is 200cm2
(a) Show that the volume Vcm3 of the block is given by
V=πr(200-πr^2)/4+2π
(b) Use calculus to find the maximum value of V. Give your answer to the nearest cm3.

(c) Justify, by further differentiation, that the value of V that you have found is a
maximum.


What are your workings?

HINT for problems like this one, you generally have to start with the information provided about area and then make a substitution in the volume formula. So what is the formula for the area of the prism?
(edited 6 years ago)
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sarah5
OP
12
Original post by BrasenoseAdm
What are your workings?

HINT for problems like this one, you generally have to start with the information provided about area and then make a substitution in the volume formula. So what is the formula for the area of the prism?


i know that but i don't know the formula of the area and the volume of this cylinder !!
Original post by sarah5
i know that but i don't know the formula of the area and the volume of this cylinder !!


OK

If it was a cylinder, then area would be

2πrh+2πr2

But it seems the shape has a semi-circle base (the question goes on about a right sided prism which is a fancy way of describing a cylinder cut down the middle, right?)



Can you see what the area is now?
(edited 6 years ago)
Reply 4
Avatar for sarah5
sarah5
OP
12
Original post by BrasenoseAdm
OK

If it was a cylinder, then area would be

2πrh+2πr2

But it seems the shape has a semi-circle base (the question goes on about a right sided prism which is a fancy way of describing a cylinder cut down the middle, right?)



Can you see what the area is now?


Ohhh yess thank you so much :smile:
Original post by sarah5
Ohhh yess thank you so much :smile:


Great!

πr^2 + πrh + 2rh

We are off home now - enjoy your evening.

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