the volume of a rectangular block of stone is 10368 dm³. its dimension are in the ratio of 3:2:1. if its entire surface is polished at 2 paisa per dm³, then find the cost incurred to polish
Answers
Step-by-step explanation:
let L=3x,b=2x, h=x
so, 3x*2x*x=6x^3
10368/6=x^3
1728=x^3
x=12
L=36, b=24 h=12
tota area to paint internal surface =2(lb+bh+lh)
=2(36*12+24*12+36*24)
=2(432+264+864)
=2(1560)
=3120
cost to paint internal surface = 3120*2=6240paisa
given:
Volume of cuboidal box= 10368dm^3
Ratio of dimensions= 3:2:1
Rate of polishing its entire surface =2 paisa per dm^2
to find:
(I) dimensions of the block
(ii) cost of polishing at the rate of 2paisa per dm^3
solution:
let the dimensions of the block be X
volume of cuboid= l*b*h
10368 = 3x * 2x * x
10368. = 6x^3
6x^3. = 10368
x^3. = 10368/6
x^3. = 1728
X= 12
therefore,
length=3*12
=36 dm
breadth=2*12
=24dm
height=1*12
=12dm
total surface area of cuboid= 2(l*b+b*h+h*l) = 2(36*24+24*12+12*36)
=2( 864+288+432)
=2*1584
=3168 dm^2
therefore,
cost of polishing its entire surface
= rate * total surface area
= 2 * 3168
= 6336 paise