The volume, total surface area and length of a diagonal of a cuboid are $V, S$ and $d$ respectively. If all edges are doubled, they become $V^{'}, S^{'}$ and $d^{'}$ respectively. Find $V^{'} : V$ , $S^{'} : S$ and $d^{'} : d$

Open in App

Solution

$V = l b h, S = 2 (l b + b h + l h), d = \sqrt{l^{2} + b^{2} + h^{2}}$
$V^{'} = (2 l) (2 b) (2 h) = 8 l b h$
$S^{'} = 2 ((2 l) (2 b) + (2 b) (2 h) + (2 l) (2 h))$
$= 4 \times 2 (l b + b h + l h)$
$d^{'} = \sqrt{(2 l)^{2} + (2 b)^{2} + (2 h)^{2}}$
$= \sqrt{4 (l^{2} + b^{2} + h^{2})} = 2 \sqrt{l^{2} + b^{2} + h^{2}}$
$\frac{V^{'}}{V} = 8; \frac{S^{'}}{S} = 4; \frac{d^{'}}{d} = 2$

Suggest Corrections

Similar questions

If l, b, h, S, and V are length, breadth, height, surface area, and volume respectively of a cuboid, then which of the following options are correct?

Two particles A and B of masses 1 kg and 2 kg respectively are kept 1 m apart and are released to move under mutual attraction. Find the speed of A when that of B is 3 cm/hour. What is the separation between the particles at this instant?

Q. The volume of a cuboid is

V

. If its length, breadth and height are made

4

times,

3

times and

2

times respectively, the volume becomes

V^{'}

. Find

V^{'} : V

Q. In a cuboid, if the sum of the lenghth of edges is represented by

S

, the total surface area is represented by

T

and the length of diagonal is represented by

D

, then the value of

D

Q. If h, S and V denote respectively the height, curved surface area and volume of a right circular cone, then

3 {πVh}^{3} - S^{2} h^{2} + 9 V^{2}

is equal to

(a) 8

(b) 0

(c) 4

π

(d) 32

π^{2}

Join BYJU'S Learning Program

The volume, total surface area and length of a diagonal of a cuboid are V,S and d respectively. If all edges are doubled, they become V′,S′ and d′ respectively. Find V′:V, S′:S and d′:d

V=lbh,S=2(lb+bh+lh),d=√l2+b2+h2V′=(2l)(2b)(2h)=8lbhS′=2((2l)(2b)+(2b)(2h)+(2l)(2h)) =4×2(lb+bh+lh)d′=√(2l)2+(2b)2+(2h)2 =√4(l2+b2+h2)=2√l2+b2+h2V′V=8;S′S=4;d′d=2

The volume, total surface area and length of a diagonal of a cuboid are $V, S$ and $d$ respectively. If all edges are doubled, they become $V^{'}, S^{'}$ and $d^{'}$ respectively. Find $V^{'} : V$ , $S^{'} : S$ and $d^{'} : d$