A pencil box has a length of 10 inches and a volume of 64 cubic inches. A similar pencil box has a volume of 512 cubic inches.
What is your question?
I will assume you want the length of the larger box, since you say they are similar..
volumes of similar objects are proportional to the cube of their corresponding sides
so , if the length of the larger box is x inches
x^3/10^3 = 512/64 = 8^3/4^3
take cube root of both sides
x/10 = 8/4 = 2
x = 20
what is the length of a pencil box by inches
To find the dimensions of the similar pencil box with a volume of 512 cubic inches, we can use the concept of geometric similarity. When two objects are similar, their corresponding dimensions are proportional.
Since the two pencil boxes are similar, we can set up a proportion to find the corresponding dimensions:
Volume of the first pencil box / Volume of the second pencil box = (Length of the first pencil box / Length of the second pencil box) cubed
Using the given information:
64 cubic inches / 512 cubic inches = (10 inches / x inches) cubed
Now, we can solve for x. Taking the cube root of both sides:
∛(64 / 512) = ∛(10 / x) cubed
∛(1/8) = 10 / x
1/2 = 10 / x
Cross-multiplying:
1x = 2 * 10
x = 20
Therefore, the length of the second pencil box is 20 inches.