Question

A large cube is constructed from individual unit cubes and then dipped into paint. Thereafter, it is disassembled into the original unit cubes; 486 of these have exactly one face painted. What is the length of a side of the large cube?

a. 6 units
b. 9 units
c. 12 units
d. 18 units

Answer 1

To find the length of a side of the large cube, we can solve the equation for surface area. The length of a side is 9 units.

Step-by-step explanation:

To solve this problem, we need to understand that the number of unit cubes with exactly one face painted is equal to the surface area of the large cube.

Let's denote the length of a side of the large cube as 'x'. The surface area of a cube is given by the formula SA = 6x^2. We are given that 486 unit cubes have one face painted, so the surface area of the large cube is 486.

Therefore, we can solve the equation 6x^2 = 486 to find the value of x. Dividing both sides by 6 gives us x^2 = 81. Taking the square root of both sides gives us x = 9.

So, the length of a side of the large cube is 9 units. Therefore, the correct answer is b. 9 units.