Answer:
Dimensions of the box are 6 in x 7 in x 8 in
Step-by-step explanation:
We will solve this question by finding the factors of 336 and seeing which factors are consecutive
Factoring 336 gives:
1 x 336
2 x 168
3 x 112
4 x 84
6 x 56
7 x 48
8 x 42 ← we can stop factoring here since 6, 7, 8 are consecutive
12 x 28
14 x 24
16 x 21
6, 7 and 8 are 3 factors which are consecutive
So the dimensions of the box are 6 in x 7 in x 8 in
To find the dimensions of the box with a volume of 336 cubic inches, we factorize the volume and find three consecutive numbers that multiply to 336, resulting in dimensions of 4 inches, 7 inches, and 12 inches.
The problem involves finding three consecutive whole numbers whose product equals the volume of a box, which is 336 cubic inches. To solve this, we need to find a set of consecutive integers that multiply to 336. Since the volume is calculated as the product of the length, width, and height of the box (Volume = length imes width imes height), we can use trial and error or factor the volume to find the dimensions.
Let's first factor 336. The prime factorization of 336 is 2 imes 2 imes 2 imes 2 imes 3 imes 7. We look for three numbers that are factors of 336 and are consecutive. We can group the prime factors into three groups that multiply to consecutive numbers: 2 imes 2 ( ext{which is } 4), 2 imes 2 imes 3 ( ext{which is } 12), and 7. Therefore, the dimensions of the box are 4 inches, 7 inches, and 12 inches.
