Question

I’ll give braniest

A small cube has the volume shown. Its side length is 2 in. less than a​ second, larger cube. What is the volume of the larger​ cube?

Answer 1

The volume of the larger cube is approximately 194.52 in^3.

Explanation:

Let's denote the side length of the larger cube as x (in inches). We know that the side length of the smaller cube is 2 inches less than the side length of the larger cube, so we can write:

side length of smaller cube = x - 2

The volume of a cube is given by the formula V = s^3, where s is the side length. Therefore, the volume of the smaller cube is:

V(smaller) = (x - 2)^3

We are given that the volume of the smaller cube is 86 in^3, so we can write:

(x - 2)^3 = 86

To solve for x, we can take the cube root of both sides:

x - 2 = ∛86

x = ∛86 + 2

Now that we know the value of x, we can find the volume of the larger cube using the formula V = s^3:

V(larger) = x^3

Substituting the expression for x, we get:

V(larger) = (∛86 + 2)^3

Using a calculator, we can evaluate this expression and get:

V(larger) ≈ 194.52 in^3

Therefore, the volume of the larger cube is approximately 194.52 in^3.