Question

The edges of a rectangular box are in the ratio 1 : 2 : 3 and its surface area is 88 cm2, the volume of the box is

Answer 1

See the attach file for ans

Answer 2

Answer:

The volume of the box is

=48cm3

Step-by-step explanation:

Given,

The edges of a rectangular box are in the ratio 1: 2 : 3

The  surface area is 88 cm2

To find,

To find the volume of the box

Let the length of the box =x, breadth =2x, height =3x

The total surface area of a box of length l, breadth b, and height $h =2(l×b+b×h+l×h)$

Step 1

The total surface area of the box = 88cm2

$2(x×2x+2x×3x+x×3x)=88cm2$

$22x2=88$

∴  $x=2$

Hence,

the length of the box =x=2cm, breadth =2x=4cm, height =3x=6cm

The volume of a box =l×b×h

Step 2

So,

The volume of the box with length =2cm,

breadth =4cm \height =6cm=2×4×6

Hence, The volume of the box is

=48cm3

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