Question

Rani has a square metal sheet. She removed squares of side 9 cm. from each corner of this sheet. Of the remaining sheet, she turned up the sides to form an open box as shown. The capacity of the box is 144 cc. Can we find out the dimensions of the metal sheet?

Answer 1

i ) Let the the side of the square sheet

= x cm

If Rani removed squares of sides of side

9 cm from each corner of the sheet .

And she turned up the sides to form an

open box .

Then , the dimensions of the box( cuboid )

length ( l ) = ( x - 2 × 9 )

= ( x - 18 ) cm

breadth ( b ) = ( x - 18 ) cm

height ( h ) = 9 cm

volume ( v ) = 144 cc ( given )

l × b × h = 144

( x - 18 )( x - 18 ) × 9 = 144

( x - 18 )² = 144/9

( x - 18 )² = 25

x - 18 = 5

x = 5 + 18

x = 23 cm

Therefore ,

Side length of the sheet

= x = 23 cm

dimensions of the box are

l = ( x - 18 ) = 23 - 18 = 5 cm

b = ( x - 18 ) = 23 - 18 = 5 cm

h = 9 cm

I hope this helps you.

: )

Answer 2

Answer:

Correct answer for x is 22.

Step-by-step explanation:

i ) Let the the side of the square sheet

= x cm

If Rani removed squares of sides of side

9 cm from each corner of the sheet .

And she turned up the sides to form an open box .

Then , the dimensions of the box( cuboid )

length ( l ) = ( x - 2 × 9 )= ( x - 18 ) cm

breadth ( b ) = ( x - 18 ) cm

height ( h ) = 9 cm

volume ( v ) = 144 cc ( given )

l × b × h = 144

( x - 18 )( x - 18 ) × 9 = 144

( x - 18 )² = 144/9

( x - 18 )² = 16

x - 18 = 4

x = 4 + 18

x = 22 cm

Therefore , Side length of the sheet= x = 22 cm

dimensions of the box are

l = ( x - 18 ) = 22 - 18 = 4 cm

b = ( x - 18 ) = 22 - 18 = 4 cm

h = 9 cm