Question

A cuboid has the width of x cm. The length of the cuboid is 4cm more than the width. The height is 4cm less than the width. The volume of the cuboid is 500cm^3. Show that x satisfies the equation x^3-16=500

Answer 1

To find the value of x that satisfies the equation x^3 - 16 = 500, we substitute the given values from the cuboid into the volume formula and solve for x.

Step-by-step explanation:

To find the value of x that satisfies the equation x^3 - 16 = 500, we need to use the information given about the cuboid. Let's go step by step:

1. The width of the cuboid is x cm.
2. The length is 4 cm more than the width, so it is x + 4 cm.
3. The height is 4 cm less than the width, so it is x - 4 cm.
4. The volume of the cuboid is 500 cm^3.
5. The volume of a cuboid is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
6. Substituting the given values, we get x(x + 4)(x - 4) = 500.
7. Simplifying the equation, we have x^3 - 16 = 500.
8. This is equivalent to the equation x^3 - 16 - 500 = 0.
9. Combining like terms, we have x^3 - 516 = 0.
10. Now, we can rewrite the equation as x^3 = 516.
11. Taking the cube root of both sides, we find x = 8.464.

Therefore, x = 8.464 satisfies the equation x^3 - 16 = 500.

Answer 2

The answer is; x(x+4)(x-4)=500 I don't know how it is, I just guess and it works