Question

A shipping box has a length of 7.00 in., a width of 6.00 in., and a height of 4.00 in. (2.3,2.6)

a. What is the length of the box, in centimeters?

b. What is the width of the box, in centimeters?

c. How many significant figures are in the width measurement?

d. Calculate the volume of the box, in cubic centimeters, to the correct number of significant figures.

Short answer

Part (a). $17.8$cm

Part (b). $15.2$cm

Part (c). $3$cm

Part (d). $2.75\times {10}^3$${\mathrm{cm}}^3$

Step-by-step solution

Part (a) Step 1: General information

Significant figures of a number in positional documentation are digits in the number that are solid and important to demonstrate the amount of something.

Part (a) Step 2: explanation 

We know

$1$inch = $2.54\mathrm{cm}$

hence,

$$\begin{gathered} 7\mathrm{in}=7\times 2.54\mathrm{cm} \\ =17.8\mathrm{cm} \end{gathered}$$

Part (b) Step 3: explanation 

We know

1 inch = $2.54\mathrm{cm}$

hence,

$$\begin{gathered} 6\mathrm{in}=6\times 2.54 \\ =15.2\mathrm{cm} \end{gathered}$$

Part (c) Step 4: explanation 

Significant figures in the width measurement are = $3$

Part (d) Step 5: explanation 

The volume is,

$\mathrm{l}\times \mathrm{b}\times \mathrm{h}$

$$\begin{gathered} =17.8\times 15.2\times 10.16 \\ =2.74\times {10}^3{\mathrm{cm}}^3 \end{gathered}$$