Question

A rectangular box has dimensions 2 in by 4 in by 4 in. Increasing each dimension of the box by the same amount yields a new box with volume five times the old. Round your answer to two decimal places

Answer 1

To find the dimensions of the larger box, assume the increase is 'x'. The new dimensions of the box will be 2+2x, 4+2x, and 4+x. Solve the resulting cubic equation to find the value of 'x' and the new dimensions of the box. Therefore, the new dimensions of the box are approximately 3.692 in by 4.692 in by 4.846 in.

Step-by-step explanation:

To find the dimensions of the larger box, we know that each dimension is increased by the same amount. Let's assume the increase is 'x'. So, the new dimensions of the box will be 2+2x, 4+2x, and 4+x. The volume of the new box is 5 times the volume of the original box, so:

(2+2x)(4+2x)(4+x) = 5(2)(4)(4)

By expanding and simplifying the equation, we get:

16x^3 + 52x^2 + 48x - 240 = 0

Now we can solve this cubic equation to find the value of 'x'. By solving the equation, we find x to be approximately 0.846. Therefore, the new dimensions of the box are approximately 3.692 in by 4.692 in by 4.846 in.