Chapter 7.1, Problem 16CYU

a.

To determine

To express: The surface area of the given cube as a monomial.

Answer to Problem 16CYU

The required surface area of the cube is $6a^6{b}^2$ .

Explanation of Solution

Given information:

Formula for the surface area of cube is $SA=6s^2$ where,

SA is the surface area and s is the length of any side.

Calculation:

  $SA=6s^2$

(Write the formula for surface area of cube)

  $=6{\left(a^{3}b\right)}^2$

(Substitute the value of s)

  $=6{\left(a^3\right)}^2{b}^2$

(Power of a product))

  $=6a^6{b}^2$

(Power of a power)

Therefore, the required surface area of the cube is $6a^6{b}^2$ .

b.

To determine

To find: The surface area of the cube if,

$a=3$

$b=4$

Answer to Problem 16CYU

The required surface area of the cube is 69984 units.

Explanation of Solution

Given information:

  $a=3$

  $b=4$

Formula for the surface area of cube is $SA=6s^2$ where,

SA is the surface area and s is the length of any side.

Calculation:

  $SA=6s^2$

(Write the formula for surface area of cube)

  $=6{\left(a^{3}b\right)}^2$

(Substitute the value of s)

  $=6{\left[\left(a^3\right)b\right]}^2$

(Substitute the values of a and b)

  $=6{\left(3^3\right)}^2{4}^2$

(Power of a product)

  $=6\cdot 3^6\cdot 4^2$

(Power of a power)

  $=69984$

(Simplify)

Therefore, the surface area of the cube is 69984 units.