Chapter 4.6, Problem 60E

(a)

To determine

To find: The volume of ink in picoliters needed to completely cover a square inch of paper.

Answer to Problem 60E

  ${10}^7\text{ picoliters}$

Explanation of Solution

Given: Inkjet printers spray droplets of ink onto paper. The volume of a single droplet is about 10 picoleters. Some printers spray as many as ${10}^6$ droplets to completely cover a square inch of paper.

Volume of 1 droplet = 10 picoliters

Spray to cover a square inch paper = ${10}^6$

So, volume of ${10}^6$ droplets $=10\times {10}^6={10}^7$ picoliters.

(b)

To determine

To find:The volume of ink to spray a square inch paper in liters.

Answer to Problem 60E

  ${10}^{-5}\text{ liter}$

Explanation of Solution

Given: Inkjet printers spray droplets of ink onto paper. The volume of a single droplet is about 10 picoleters. Some printers spray as many as ${10}^6$ droplets to completely cover a square inch of paper. There are ${10}^{12}$ picoliters in a liter.

To spray a square inch paper = ${10}^7$ picoliters.

Now, change this into liter.

In ${10}^{12}$ picoliters = 1 liter

In 1 picoliter $=\frac{1}{{10}^{12}}\text{ liters}$

In ${10}^7$ picoliters $=\frac{{10}^7}{{10}^{12}}={10}^{-5}\text{ liter}$

(c)

To determine

To find: The area of paper to the nearest power of 10 and find the volume of ink.

Answer to Problem 60E

  ${10}^{-3}\text{ liter}$

Explanation of Solution

Given: Inkjet printers spray droplets of ink onto paper. The volume of a single droplet is about 10 picoleters. Some printers spray as many as ${10}^6$ droplets to completely cover a square inch of paper. There are ${10}^{12}$ picoliters in a liter. The dimension of paper 8.5 in by 11 in.

The shape of paper is rectangle whose dimension is 8.5 in by 11 in

Area of paper piece $=8.5\times 11={10}^2{\text{ in}}^2$

To spray a square inch paper = ${10}^{-5}$ liter

To spray ${10}^2{\text{ in}}^2$ = ${10}^2\times {\text{10}}^{-5}{\text{=10}}^{-3}\text{ liter}$

Hence, ${10}^{-3}\text{ liter}$ ink needed to spray entire piece of paper.

(d)

To determine

To find: The number of pages can print if cartridge contains 60 milliliters of ink.

Answer to Problem 60E

  $60\text{ pages}$

Explanation of Solution

Given: Inkjet printers spray droplets of ink onto paper. The volume of a single droplet is about 10 picoleters. Some printers spray as many as ${10}^6$ droplets to completely cover a square inch of paper. There are ${10}^{12}$ picoliters in a liter. The dimension of paper 8.5 in by 11 in.

  ${10}^{-3}\text{ liter}$ = 1 milliliter

In part (c), calculated each page needed 1 milliliter of ink.

In 1 milliliter = 1 page print

In 60 milliliters $=60\times 1=60\text{ pages}$

Hence, 60 pages print by an inkjet cartridge contains 60 milliliters of ink.