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.

[ Ans : 4.255, 8.56×10]​

Answer 1

Given:

Length (Z) = 4.234 m

Breadth (b) = 1.005 m

Thickness

d = 2.01 cm = 2.01 x $10^{-2}$ m

Formula To Find Area Of Sheet:

2 (lb + bd + dl)

Solving Using This Formula:

= 2(4.234 x 1.005 +1.005 x 0.0201 + 0.0201 x 4.234)

= 2(4.3604739) = 8.7209478 m^2

As the least number of significant figure in thickness is 3. Therefore, area has 3 significant  figure

Area = 8.72 m^2

Volume Of Metal Sheet = Z x b x d

= 4.234 x 1.005 x 0.0201 m^3

= 0.085528917 m^3

After rounding off = 0.0855 m^3

Answer 2

$\bigstar$ 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.

$\bigstar$ Given:

• Length = 4.325 m
• Breadth = 1.005 m
• Thickness = 2.01 cm

$\bigstar$ To Find:

• Significant value of area
• Significant value of volume

$\bigstar$ Solution:

The length has 4 significant figures.

The breadth has 4 significant figures.

The height has 3 significant figures.

Formulae: $\sf 2(l \times b + b \times h + h \times l)$

$\implies \sf 2(4.325 \times 1.402 + 1.402 \times 0.0312 + 0.0312 \times 4.325)$

$\implies \sf 2(6.06365 + 0.0437424 + 0.13494)$

$\implies\sf 2\times 6.2423$

$\implies \sf 12.484 \: m^{2}$

Volume: $\sf l\times b\times h$

$\implies \sf 4.325 \times 1.402 \times 0.0312$

$\implies \sf 0.189^{3}$

Therefore,

The volume has three significant values 1, 8 and 9.

The area has five significant values 1, 2, 4, 8 and 4.

$\bigstar$ Points to Note:

➤ The formula for surface area is $\sf 2(l \times b + b \times h + h \times l)$

➤ The term stands for International System of Units which has regulated seven base units to be used to represent quantity .

➤ Significant figures refers to the number of important single digits in the coefficient of expression in the scientific notation.