Question 1.31 - Chemistry: Molecular Nature Of Matter And Change

Question

The area of a telescope lens is $\mathbf{7903}\mathbf{ }{\mathbf{mm}}^{\mathbf{2}}$.

(a) What is the area in square feet (${\mathbf{ft}}^{\mathbf{2}}$ )? 

(b) If it takes a technician 45 s to polish $\mathbf{135}\mathbf{ }{\mathbf{mm}}^{\mathbf{2}}$ , how long does it take her to polish the entire lens?                      

Step-by-Step Solution

Answer

Answer:

 

Thus, the time required for polishing $7903 {\mathrm{mm}}^2$  area will be 2634.33 s.

Conversion unit involved.

 Conversion units are used to transform the measurement to the same unit. Feet can be converted to mm by multiplying with 304.8. 

The conversion unit can be thus written as: 

Conversion of foot to mm

Since the given length is in feet, it can be converted to mm as:

$$\begin{gathered} 1 m{m}^2 =1.07639 \times {10}^{-5} f{t}^2 \\ Conversion factor =\frac{1.07639 \times {10}^{-5} f{t}^2}{1 m{m}^2} \\ \mathrm{Length} \mathrm{in} f{t}^2 = \mathrm{Length} \mathrm{in} m{m}^2 \times \mathrm{Conversion} \mathrm{factor} \\ \mathrm{Length} \mathrm{in} f{t}^2\mathit{ }= 7903 \cancel{m{m}^2} \times \left(\frac{1.07639 \times {10}^{-5} f{t}^2}{1\cancel{ m{m}^2}}\right) \\ \mathrm{Hence}, \\ \mathrm{Length} = 0.0851 f{t}^2 \end{gathered}$$

Thus the area in square feet is 0.0851 ${\mathbf{ft}}^{\mathbf{2}}$.

Calculate the time taken to polish the entire lens

The given time to polish the area of $135 {\mathrm{mm}}^2$ is 45 s. Thus the time required to polish $7903 {\mathrm{mm}}^2$ can be calculated as:

$$\begin{gathered} \mathrm{Time} \mathrm{of} \mathrm{polishing} 135 m{m}^2 \mathrm{area} = 45s \\ \mathrm{Time} \mathrm{of} \mathrm{polishing} 1 m{m}^2 \mathrm{area}=\frac{45s}{135 m{m}^2} \\ \mathrm{Time} \mathrm{of} \mathrm{polishing} 7903 m{m}^2 \mathrm{area} =\frac{45\mathrm{s}}{135 \cancel{{\mathrm{mm}}^2}} \times 7903 \cancel{{\mathrm{mm}}^2} \\ = 2634.33 s \\ \mathbf{Thus}\mathbf{,}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{time}\mathbf{ }\mathbf{required}\mathbf{ }\mathbf{for}\mathbf{ }\mathbf{polishing}\mathbf{ }\mathbf{7903}\mathbf{ }{\mathbf{mm}}^{\mathbf{2}}\mathbf{ }\mathbf{area}\mathbf{ }\mathbf{will}\mathbf{ }\mathbf{be}\mathbf{ }\mathbf{2634}\mathbf{.}\mathbf{33}\mathbf{ }\mathbf{s}\mathbf{.} \end{gathered}$$