Question

You are designing a chocolate mold shaped like a hollow rectangular prism fora candy manufacturer. The mold must have a thickness of 1 centimeter in all dimensions. The mold's outer dimensions should also be in the ratio 1:3:6. What should the outer dimensions of the mold be if it is to hold 112 cubic centimeters of chocolate?

Answer 1

To find the dimensions of the rectangular prism mold, we can set up and solve an equation using the given volume and the ratio of the outer dimensions. The outer dimensions of the mold, including the thickness, are (x+2) cm, (3x+2) cm, and (6x+2) cm.

Step-by-step explanation:

To solve this problem, we need to find the dimensions of the rectangular prism. Let's assume that the length of the prism is x. According to the ratio, the width is 3x and the height is 6x. The outer dimensions of the mold, including the thickness, would be (x+2) cm, (3x+2) cm, and (6x+2) cm.

Next, we can calculate the volume of the mold using the formula for the volume of a rectangular prism: V = length * width * height. We know that the volume is 112 cubic centimeters, so we can set up the equation: (x+2) * (3x+2) * (6x+2) = 112.

Now, we can solve the equation for x to find the dimensions of the mold.

Answer 2

To find the outer dimensions of the chocolate mold, we need to calculate the length, width, and height of the mold using the given information. The outer dimensions of the mold should be approximately 1.795 centimeters by 3 * 1.795 centimeters by 6 * 1.795 centimeters.

Step-by-step explanation:

To find the outer dimensions of the chocolate mold, we need to calculate the length, width, and height of the mold using the given information. Let x be the common ratio for the outer dimensions of the mold. So, the length, width, and height of the mold would be x, 3x, and 6x respectively.

The volume of the mold can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. We are given that the volume should be 112 cubic centimeters, so we can write the equation:

112 = x * 3x * 6x

Now, we can solve for x in the equation:

112 = 18x^3

x^3 = 6.2222...

x ≈ 1.795

Therefore, the outer dimensions of the mold should be approximately 1.795 centimeters by 3 * 1.795 centimeters by 6 * 1.795 centimeters.