sir, please give me the proper solution with explation of following questions Q A box with lid is made - Maths - Mensuration

Question

sir, please give me the proper solution with explation of
following questions?
Q A box with lid is made of wood which is 3 cm thick It's
external length,breadth and hieht are 56 cm,39 cm and 30 cm
respectively Find the capacity of the box Also find the volume of
wood used to make this box
Q If V is the volume of cuboid of dimension a,b and c and S is
it's surface area , then prove that:-
1/v =2/s [1/a +1/b +1/c]

Gursheen kaur. · Accepted Answer

SOLUTION 1)

We have a cuboidal box with external dimensions (56cm x 39cm x 30cm)

The thickness of the wood in the box = 3 cm.

The box is open from one end.

∴ The internal dimensions are (50cm x 33cm x 27cm) as the box is considered to be open along its height at one end

The capacity of the box

$= (l) (b) (h) = (50) (33) (27) = 44550 {c m}^{3}$

Volume of wood

$= E x t e r n a l V o l u m e - I n t e r n a l V o l u m e = [(56) (39) (30) - (50) (33) (27)] = (65520 - 44550) {c m}^{3} = 20970 {c m}^{3}$

SOLUTION 2)

Volume of cuboid,V= abc ...........(i)

Surface area of cuboid,S= 2(ab+bc+ca) .......(ii)

Now, On Dividing (ii) by (i), we get,

$\frac{S}{V} = \frac{2 (a b + b c + c a)}{a b c} \Rightarrow \frac{1}{V} = \frac{2 (a b + b c + c a)}{S (a b c)} \Rightarrow \frac{1}{V} = \frac{2}{S} (\frac{a b}{a b c} + \frac{b c}{a b c} + \frac{c a}{a b c}) \Rightarrow \frac{1}{V} = \frac{2}{S} (\frac{1}{c} + \frac{1}{a} + \frac{1}{b}) \Rightarrow \frac{1}{V} = \frac{2}{S} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$