Chapter 7.3, Problem 42PPE

To determine

To find: The volume of the cylinder and write the answer in scientific notation.

Answer to Problem 42PPE

The required volume of the cylinder is $6.5\times {10}^{-8}{m}^3$ .

Explanation of Solution

Given information:

The radius (r) of a cylinder is $7.8\times {10}^{-4}$ m.

The height (h) of the cylinder is $3.4\times {10}^{-2}$ m.

Calculation:

We know, volume of a cylinder $=\pi r^{2}h$

  $=3.14\cdot {\left(7.8\times {10}^{-4}\right)}^2\cdot \left(3.4\times {10}^{-2}\right)$

(Substitute the value of radius and height)

  $=3.14\cdot \left({7.8}^2\cdot {10}^{-4\cdot 2}\cdot 3.4\cdot {10}^{-2}\right)$

(Raise the two factors to the second power)

  $=3.14\cdot {7.8}^2\cdot {10}^{-8}\cdot 3.4\cdot {10}^{-2}$

(Multiply the exponents of a power raised to a power)

  $=3.14\cdot {7.8}^2\cdot {10}^{-8}\cdot {10}^{-2}\cdot 3.4$

(Use the commutative property of multiplication)

  $=3.14\cdot {7.8}^2\cdot 3.4\cdot {10}^{-8+\left(-2\right)}$

(Add exponents of powers with the same base)

  $=6.4952784\times {10}^{-8}$

(Simplify)

Therefore, the volume of the cylinder is $6.5\times {10}^{-8}{m}^3$ .