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1. 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---
2. (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?
3. (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
4. (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
5. (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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