Home
Class 10
MATHS
A rectangular sheet of tin 58 cmxx44cm i...

A rectangular sheet of tin 58 `cmxx44cm` is to be made into an open box by cutting off equal squares from the corners and folding up the flaps.What should be the volume of box if the surface area of box is 2452 `cm^(2)`?

Text Solution

Verified by Experts

Let square of x cm from each corner be removed form a rectangurlar sheet
So, length of box = (58-2x) cm
breadth of box=(44-2x) cm
and height of box = x cm
surface area of open box = 2(lb+bh+hl)-lb
`2[(58-2x)(44-2x)+x(44-2x)+x(58-2x)]-(58-2x)(44-2x)=2452`
(58-2x)(44-2x)+x(22-x)+x(29-x)=2452
(29-x(22-x)+xc(22-x)+x(29-x)=613
`638-51x+22x-x^(2)+29x-x^(2)=613`
`x^(2)=25`
x=5cm
(x=-5 is not admissible)
(volume of box `=58-2x)(44-2x)=5(58-10)(44-10)`
`=5xx48xx34cm^(3)=8160 cm^(3)`
Promotional Banner

Topper's Solved these Questions

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/exemplar|10 Videos

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|68 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Questions|1 Videos

Similar Questions

Explore conceptually related problems

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top by cutting off squares from the corners and folding up the flaps. What should be the side of the square in order the volume of the box is maximum.

A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Also, find the maximum volume.

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?

A square piece of cardbroad measuring x inches by x inches is to be used to form an open box by cutting off 2-inch squares, and then folding the slides up along the dotted lines, as shown in the figure above. If x is an integer , and the volume of the box must be greater than 128 cubic inches , what is the smallest value of x that can be used ?

A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. The value of x os that volume of the box is maximum is (a) 1 (b) 2 (c) 3 (d) 4

A box of maximum volume with top open is to be made by cutting out four equal squares from four corners of a square tin sheet of side length a feet and then folding up the flaps. Find the side of the square cut-off.

An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

From a rectangular sheet of tin, of size 100 cm by 80 cm, are cut four squares of side 10 cm from each corner. Find the area of the remaining sheet.

A square sheet of side 5cm is cut out from a rectangular piece of an aluminium sheet of length 9cm and breadth 6cm. What is the area of the aluminium sheet left over?

A metallic sheet is of the rectangular shape with dimensions 48cm xx 36cm . From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.