Question

Which monomial represents the number of square units in the area of a circle with radius 4x^3 units

Answer 1

The area of a circle with radius 4x^3 units is represented by the monomial 16πx^6 square units.

Step-by-step explanation:

The monomial representing the number of square units in the area of a circle with radius 4x^3 units can be found by using the area formula for a circle, which is A = πr². When substituting 4x^3 for r, the area formula becomes A = π(4x^3)². By squaring the radius, we get A = π(16x^6), which simplifies to the monomial 16πx^6 square units. This represents the area of the circle.

Answer 2

For a circle of radius R, the area is written as:

A = pi*R^2

Where pi = 3.14

Then if the radius of the circle is R = 4*x^3

The area of this circle will be:

A = 3.14*(4*x^3)^2 = 3.14*(4)^2*(x^3)^2

Here you need to remember that:

(a^n)^m = a^(n*m)

Then the area of the circle is:

A = 3.14*(16)*(x^(3*2) = 3.14*16*x^6 = 50.24*x^6

So the monomial that represents the number of square units in the area of the circle is:

A(x) = 50.24*x^6