Assume that you want to construct a box with a square base (closed top) and a volume of 1000 cm3 . Find the dimensions of the box to minimize the surface area of the box.

Step-by-step explanation:

The Volume of a box with a square base  

x by  x  cm and height  h  cm is  

V =x^2h

The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.

The surface area of the box described is  

A = x ^2 +4 x h

We need  

A  as a function of  x  alone, so we'll use the fact that

V= x^2h = 1000 cm^3

This imples  

This makes

Differentiating A w.r.t. x

Now, A'=0

Therefore, minimum value x =

answer:

total cost for tiles and paints is $924.  

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

given: 1m squared floor tiles costs $3. so,

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

therefore, the combined total cost of tiles and paint is $924.