Chapter 7.1, Problem 59PPS

To determine

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

Answer to Problem 59PPS

The required volume of the solid is $15x^7$ units.

Explanation of Solution

Given information:

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,

  $l=5x^3$

  $b=3x^2$

  $h=x^2$

  $V=l\cdot b\cdot h$

(Write the formula)

  $=\left(5x^3\right)\left(3x^2\right)\left(x^2\right)$

(Substitute the values of l, b and h)

  $=5\cdot 3\cdot x^3\cdot x^2\cdot x^2$

(Commutative)

  $=5\cdot 3\cdot x^7$

(Product of powers)

  $=15x^7$

(Simplify)

Therefore, the volume of the cuboid is $15x^7$ units.