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Maths a level differentiation please help

8) a cuboid has a square base of length x metres and heigh y metres
a) express the volume V of the cuboid in terms of x and y
b) show that the surface area of the cuboid is 2x^2 + 4xy
- the surface area of the cuboid is 24cm ^2 -
c) show that v = 6x - 0.5x^3
d) show that the maximum volume of the box occurs when x = 2 and find this maximum volume

---Moved to maths---
(edited 7 years ago)
Reply 1
Avatar for Naruke
Naruke
11
Original post by imaan2121
8) a cuboid has a square base of length x metres and heigh y metres
a) express the volume V of the cuboid in terms of x and y
b) show that the surface area of the cuboid is 2x^2 + 4xy
- the surface area of the cuboid is 24cm ^2 -
c) show that v = 6x - 0.5x^3
d) show that the maximum volume of the box occurs when x = 2 and find this maximum volume

---Moved to maths---


Sketch the cuboid, so you have something to reference back to during your workings.

a) Do you know the formula for the volume of a cuboid?

b) Do you know the formula for the surface area of a cuboid?

What part are you stuck on exactly?
Reply 2
Avatar for imaan2121
imaan2121
OP
9
Original post by Naruke
Sketch the cuboid, so you have something to reference back to during your workings.

a) Do you know the formula for the volume of a cuboid?

b) Do you know the formula for the surface area of a cuboid?

What part are you stuck on exactly?


I got the volume as x^2y, but don't know how the surface are = 2x^2 + 4y
Reply 3
Avatar for MrIso
MrIso
10
Original post by imaan2121
I got the volume as x^2y, but don't know how the surface are = 2x^2 + 4y


Imagine this cuboid with two square faces that have length and width x and x and four other faces with length and width x and y. The area of the faces that are square is equal to the length multiplied by the width so it will be x*x, which is x^2. As there are two squares faces you multiply this by two to get 2x^2.

Afterwards, you obtain the area of the other faces by multiplying x by y, getting xy. As there are four faces, you multiply this by 4 to get 4xy.

As this is total surface area, you must add all of the surface areas together, which adds up to 2x^2 + 4xy
(edited 7 years ago)
Original post by imaan2121
8) a cuboid has a square base of length x metres and heigh y metres
a) express the volume V of the cuboid in terms of x and y
b) show that the surface area of the cuboid is 2x^2 + 4xy
- the surface area of the cuboid is 24cm ^2 -
c) show that v = 6x - 0.5x^3
d) show that the maximum volume of the box occurs when x = 2 and find this maximum volume

---Moved to maths---


Rewrite yor answer to a and sub into the result for b to get c.
Differentiate and set to 0 to find d.

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