A metal box with a square base and verti...

A metal box with a square base and vertical sides is to contain `1024c m^3` of water, the material for the top and bottom costs Rs. `5p e rc m^2` and the material for the costs Rs. `2. 50p e rc m^2` . Find the least cost of the box.

Text Solution

Verified by Experts

The correct Answer is:

1920

Topper's Solved these Questions

DIFFERENTIAL CALCULUS 2
VMC MODULES ENGLISH|Exercise Level -2|69 Videos
DIFFERENTIAL CALCULUS 2
VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|14 Videos
DIFFERENTIAL CALCULUS 2
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos
DIFFERENTIAL CALCULUS
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos
DIFFERENTIAL EQUATIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

A metal box with a square base and vertical sides is to contain 1024 cm3 of water, the material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box.

The cost of one metre cloth is Rs 24.75 . Find the cost of 2.8 m cloth.

2.25 m of a cloth costs Rs 326.25 What is the cost of 1m of cloth ?

If a cloth costs Rs 715 1/4 per metre, find the cost of 3 2/5 metres of this cloth.

An open tank with a square base and vertical sides is to be constructed form a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of tank is half its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided, what kind of value is hidden in the question

If 1 metre cloth costs Rs. 31""3/4 , find the cost of 5""1/2 metres cloth.

The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of R s\ 0. 50\ p e r\ m^2 . Find the cost of ploughing the field .

A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 m3. If building of tank costs Rs. 100 per square metre for the base and Rs. 50 per square metres for the sides, find the cost of least expensive tank.

A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 "m"^3 . If building of tank costs Rs. 100 per square metre for the base and Rs. 50 per square metre for the sides, find the cost of least expensive tank.

The dimensions of a rectangular box are in the ratio 2:3:4 and the difference between the cost of covering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m^2 is Rs. 1248. Find the dimensions of the box.

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -1

Let f(x)=8x^(3)-6x^(2)-2x+1, then
Text Solution
|
Show that semi-vertical angle of a cone of maximum volume and given sl...
Text Solution
|
Show that semi-vertical angle of right circular cone of given total su...
Text Solution
|
A window is in the shape of a rectangle surmounted by a semi circle. I...
Text Solution
|
A window of perimeter P (including the base of the arch) is in the ...
Text Solution
|
about to only mathematics
Text Solution
|
The total area of a page is 150c m^2dot The combined width of the marg...
Text Solution
|
In a submarine telegraph cable the speed of signaling varies as x^2log...
Text Solution
|
A wire of length l is cut into two parts. One part is bent into a circ...
Text Solution
|
A running track of 440 ft is to be laid out enclosing a football field...
Text Solution
|
If a cone of maximum volume is inscribed in a given sphere, then th...
Text Solution
|
Find the maimum distacne of norma to ellipse (x^(2))/(a^(2))+(y^(2))/(...
Text Solution
|
If a circle of radius 'a' inside an equilateral triangle, then prove t...
Text Solution
|
A metal box with a square base and vertical sides is to contain 102...
Text Solution
|
Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...
Text Solution
|
A window is in the shape of a rectangle surmounted by a semi circle. I...
Text Solution
|
The height of a right circular cylinder of maxium volume inscribed in ...
Text Solution
|
All possible value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) ...
Text Solution
|
The difference between the greatest and least value of the functions, ...
Text Solution
|
If f(x)=a(0)+a(1)x^(2)+a(2)x^(4)+...+ a(n)x^(2n) be a polynomial where...
Text Solution
|