Chapter 7.1, Problem 60PPS

To determine

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

Answer to Problem 60PPS

The required volume of the solid is $16x^8$ units.

Explanation of Solution

Calculation:

The given solid is a cuboid..

The formula for the volume of a cuboid is $V=l\cdot b\cdot h$ where,

V is the volume, l is the length, b is the width and h is the height.

From the given diagram we get,

  $l=2x^2$

  $b=2x^2$

  $h=4x^4$

  $V=l\cdot b\cdot h$

(Write the formula)

  $=\left(2x^2\right)\left(2x^2\right)\left(4x^4\right)$

(Substitute the values of l, b and h)

  $=2\cdot 2\cdot 4\cdot x^2\cdot x^2\cdot x^4$

(Commutative)

  $=2\cdot 2\cdot 4\cdot x^8$

(Product of powers)

  $=16x^8$

(Simplify)

Therefore, the volume of the cuboid is $16x^8$ units.