the dimensions of base of a rectangular box of greatest volume that can be constructed from 100 cm s&#8230;.
the dimensions of base of a rectangular box of greatest volume that can be constructed from 100 cm square of hard board sheet, if the box is three times as long as it is wide, are \_\_\_\_\_\_.
the dimensions of base of a rectangular box of greatest volume that can be constructed from 100 cm square of hard board sheet, if the box is three times as long as it is wide, are \_\_\_\_\_\_.
you don't say that the area must be a rectangle. the true largest area would be a circle, with the circumference equal to 400m and the area would be 12,732.4 m^2. however, evidently, the area is restricted to a rectangle, in which case the maximum area is a square, and the side of the square will be 
400/4 = 100 m. the area is 100x100 = 10,000 m^2.
algebraically,
let x = one pair of opposite sides
(400-2x)/2 = 200-x = the other pair of opposite sides

area = a(x) = x(200 - x) = -x^2 + 200x
x-coordinate of vertex = -b/2a = 200/2 = 100
a(100) = 10,000

that's it! ;) given: volume of cylinder = 1617 cm3let r be the radius of base and h be the height of coner:h = 2:3∴ r/h = 2/33r = 2hh = 3r/2 …(i)formula: volume of cylinder = πr2h∴ 1617 = (22/7) r2hr2h = 514.5using (i) we have∴ r2 × (3r/2) = 514.53r3 = 1029r3 = 343r = 7 cmh = 21/2 cmtotal surface area of cylinder = 2πr2 + 2πrh= 2 × (22/7) × 72 + 2 × (22/7) × 7 × (21/2)= 308 + 462= 770 cm2therefore total surface area of cylinder = 770 cm2 given:volume of given cube = 64cm3side = a cmvolume = (a)364 = (a)3a = 4cmtwo cubes are joined together.length of resultant cube = 4+4 = 8cmbreadth = 4cmheight = 4cm(a) lsa of cuboid = 2(lh+hb)= 2(8(4) + 4(4))= 2(32+16)= 2(48) = 96cm2⇒ lsa of cuboid = 66m2(b)tsa of cuboid = 2(lh+hb+lb)= 2(8(4) + 4(4) + 8(4))= 2(32+16+32)⇒ tsa of cuboid = 2(80) = 160m2 radius = 1.75 m
height (h) = 12 m
volume = 
= ×  × 1.75 × 1.75 × 12
= 38.5 m3
since, 1 m3 = 1 kiloliter
capacity of the pit = (38.5 × 1)
= 38.5 kilolitres the sides of the triangle are 6 cm, 8 cm and 10 cm. the longest side is 10 cm. (10)2 = 100 ….(i) now, the sum of the squares of the other two sides will be, (6)2 + (8)2 = 36 + 64 = 100 ….(ii) (10)2 = (6)2 + (8)2 ….. from (i) and (ii) by the converse of pythagoras theorem: the given sides form a right angled triangle. given radius of cone (r) = 3.5/2 m height of cone (h) = 12 m find out we have to find the capacity in kiloleters solution volume of cone = (1/3) × πr2h on taking π=22/7 = (1/3) × (22/7) × (3.5/2) × (3.5/2) × 12 = (22 × 3.5 × 3.5 × 12) / (7 × 3 × 2 × 2) = 38.5 m3 capacity of conical pit in kilo liters: 1000 m3 = 1 liter 38.5 m3 = 1000 × 38.5 liters = 38,500 liters = 38.5 kilo liters answer the capacity of the container is 38.5 kilo liters Notice that the matrix A is upper-triangle, so its determinant is a  
product   
of diagonal elements:  
  
det(A) = 1*2*3 = 6.  
  
Moreover, det(A) is   
non-zero.  
Therefore the columns of A are linearly independent and   
therefore  
they constitutive a basis for R^3, so R^3 = Col(A).  
  
Hence   
any base of R^3 fits to be a base for Col(A),   
for instance the columns of   
A:  
  
(1,0,0), (2,2,0), (3,3,3)  
  
or   
  
(1,0,0), (0,1,0),   
(0,0,1)  
  
are the base.  
  
The dimension of Col(A) is the dimension of   
R^3 and therefore is equal  
to 3. a. dimensions of h = [l]dimensions of s = [mt-2]dimensions of ρ = [ml-3]dimensions of r = [l]dimensions of g = [lt-2]checking the r.h.sdimensionally= = [m0l1t0]a. is dimensionally correctb. dimensions of v = [lt-1]dimensions of p = [ml-1t-2]dimensions of ρ = [ml-3]checking the r.h.sdimensionally= b. is dimensionally correctc. dimensions of v = [l3]dimensions of p = [ml-1t-2]dimensions of r4 = [l4]dimensions of t = [t]dimensions of l = [l]dimensions of η = [ml-1t-1]checking the r.h.sdimensionally= =[l3]c. is dimensionally correctd. dimensions of v = [t-1]dimensions of m = [m]dimensions of g = [lt-2]dimensions of l = [l]dimensions of i = [ml2]checking the r.h.sdimensionally= d. is dimensionally correct Correct option is A) 9.378 m2


![](https://lh3.googleusercontent.com/-UueuqyijXPQ/YLtK0v0m9CI/AAAAAAAABro/xFcfQOQAOx8jHAtpqiORvW_8DRFX1yK3ACLcBGAsYHQ/image.png)


result must have significant figures equal to least figures being multiplid do area of metal sheet 9.378 m2  (four significant digits) the collection of images type of tileset can contain tiles of any size. when the tiles are larger than the map grid, they extend beyond their cell, overlapping other tiles. they still occupy only a single cell on the tile layer.

larger tiles than the grid are commonly used to make it easier to plac…