Question

the volume of a cubical solid is 10368 cm cube if its dimensions are in the ratio 3 : 2 : 1 find the find the cost of polishing its total surface @ rupees 2.5 per metre square

Answer 1

let the common factor be x

length=3x
breadth=2x
height=x

volume=l×b×h

$10368 = 3x \times 2x \times x$

$13068 = 6 {x}^{3}$
${x}^{3} = \frac{10368}{6}$

${x}^{3} = 1728$

$x = \sqrt[3]{1728}$
$x = 12$
length=3x=12×3=36cm =0.36m
breadth=2x=2×12=24cm=0.24m
height=x=12cm=0.12m

total surface area=2(lb+bh+lh)
=2(0.36×0.24+0.24×0.12+
0.36×0.12)
=2(0.1584)
=0.3168m^2

cost for 2.5 m^2
=0.3168×2.5
=0.792m^2