Question

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

Answer 1

Given, the length of the rectangular sheet is 4.234 m , breadth of the rectangular sheet is 1.005 m and thickness of the rectangular sheet is 2.01 cm .

Let the length, breadth and thickness of the rectangular sheet are l, b and t.

The area of the rectangular sheet is,

A=2( l×b+b×t+t×l )

Substitute the given values in the above expression.

A=2×( 4.234 m×1.005 m+1.005 m×2.01 cm× 10 −2  m 1 cm +2.01 cm× 10 −2  m 1 cm ×4.234 m ) =( 4.25517+0.0202005+0.0851034 )  m 2 =8.7209478

Since the significant figure of length and breadth are 4 and the significant figure of thickness is 3. So, the significant figure for the area of the rectangular sheet must be 3.

Hence, the area of the rectangular sheet is 8.72  m 2

The volume of the rectangular sheet is,

V=l×b×t

Substitute the given values in the above expression.

V=4.234 m×1.005 m×2.01 cm× 10 −2  m 1 cm =0.085528917  m 3

Since the significant figure of length and breadth are 4 and the significant figure of thickness is 3. So, the significant figure of the volume of the rectangular sheet must be 3. Hence, the volume of the rectangular sheet is 0.0855  m 3