Chapter 7.1, Problem 58PPS

To determine

To express: The volume of the given solid as a monomial.

Answer to Problem 58PPS

The required volume of the solid is $113.04x^4$ units.

Explanation of Solution

Given information:

Calculation:

The given solid is a cylinder.

The formula for the volume of a cylinder is $V=\pi r^{2}h$ where,

V is the volume, r is the radius and h is the height of the cylinder.

From the given diagram we get,

  $Radius=2x$

  $Height=3x^2$

  $V=\pi r^{2}h$

(Write the formula)

  $=\pi \cdot {\left(2x\right)}^2\cdot 3x^2$

(Substitute the value of r and h)

  $=\pi \cdot 2^2\cdot x^2\cdot 3x^2$

(Power of product)

  $=\pi \cdot 2^2\cdot 3^2\cdot x^2\cdot x^2$

(Commutative)

  $=\pi \cdot 2^2\cdot 3^2\cdot x^4$

(Product of powers)

  $=3.14\cdot 2^2\cdot 3^2\cdot x^4$

(Substitute the value of $\pi$ i.e. 3.14)

  $=113.04x^4$

(Simplify)

Therefore, the volume of the cylinder is $113.04x^4$ units.