An open box with a square base is to be made out of a given
quantity of sheet of area `a^2`, Show the maximum volume of the
box is `frac {a^3}{6 sqrt 3}`

A box with a square base is to have an open top. The surface area of the box is 192 sq.cm. What should be its dimensions in order that the volume is largest?

An open box is to be cut of piece of square card board of side 18 cm by cutting of equal squares from the corners and turning up the sides. Find the maximum volume of the box.

An open box of length 1.5m, breadth 1m, and height 1m is to be made for use on a trolly for carrying garden waste. How much metal sheet will be required to make this box? The inside and outside surfaces of the box are to be painted with rust proof paint. What will be the cost to paint the box at the rate of $ 150 per square metre?

An open cylindrical tank whose base is a circle is to be constructed of metal sheet so as to contain a volume of pi a^3 cu. cm of water. Find the dimensions so that sheet required is minimum.

A closed right circular cylinder of given total surface area, has maximum volume when height (h) is...... A) h=2r B) h=r C) h=3r D) h= sqrt (2r)

Given two squares of sides x and y such that y=x+x^(2) what is the rate of change of area of the second square with respect to the area of the first square? a) x^2+3x-1 b) 2x^2-3x+1 c) 2x^2+3x+1 d)1+2x

Choose the correct alternative from those given below each question: Which of the following is the value of the discriminant for 2x^2 +5sqrt3x+6=0