Question

What is the number of cubic inches in one cubic foot?

Answer 1

Hint: In this question, we are given the volume as one cubic foot and we have to find the number of cubic inches in that volume. Therefore, we should divide the volume of one cubic foot by one cubic inch to get the required answer to this question.

Complete step by step answer:
We know that 1 foot = 12 inches
Therefore number of inches in one foot = 12 …………………..(1.1)
We know that
1 cubic foot = 1 foot $\times $ 1 foot $\times $ 1 foot ………………………………(1.2)
Therefore, using equation (1.1) and (1.2), we can write
Total number of inches in one cubic foot = number of inches in one foot $\times $ number of inches in one foot $\times $ number of inches in one foot
= 12 $\times$ 12 $\times$ 12
= 1728 …………………….(1.3)

Therefore, there are 1728 cubic inches in one cubic foot which should be the required answer to this question.

Note: We should be careful to multiply the factor for obtaining the number of inches in one foot thrice in equation (1.3) and not just multiplying it one time as while taking a cube of a quantity, the unit of the quantity is also multiplied three times. Thus the factor of 12 should be multiplied 3 times in equation (1.3) to obtain the required answer. Do not make the mistake of using the relation as 1 foot = $\dfrac{1}{12}$ inches as it is not correct.