The volume of a cube is 64 cubic inches. Which expression represents the length of a side of the cube?
Answer (2)
The volume of the cube is given as 64 cubic inches.
The formula for the volume of a cube is V = s 3 , where s is the side length.
To find the side length, take the cube root of the volume: s = 3 V = 3 64 .
Calculate the cube root: s = 4 inches. The expression representing the length of a side of the cube is 4 .
Explanation
Problem Analysis and Correct Formula The problem states that the volume of a cube is 64 cubic inches and asks for the expression that represents the length of a side of the cube. The formula V = S 2 provided in the question is incorrect. The correct formula for the volume of a cube is V = s 3 , where V is the volume and s is the side length.
Given Volume We are given that the volume V of the cube is 64 cubic inches. We need to find the side length s such that s 3 = 64 .
Taking the Cube Root To find the side length s , we take the cube root of both sides of the equation s 3 = 64 . This gives us s = 3 64 .
Calculating the Cube Root The cube root of 64 is 4, since 4 × 4 × 4 = 64 . Therefore, s = 3 64 = 4 inches.
Final Answer The expression representing the length of a side of the cube is 3 64 , which simplifies to 4 inches.
Examples
Imagine you're building a cubic storage box and you know it needs to hold exactly 64 cubic inches of items. To figure out how long each side of the box needs to be, you calculate the cube root of 64, which is 4 inches. This tells you that each side of the box should be 4 inches long to achieve the desired volume. This concept is useful in various fields like packaging, construction, and even in creating art installations where precise cubic volumes are required.
The length of a side of the cube, given its volume of 64 cubic inches, is represented by the expression 3 64 which simplifies to 4 inches. Thus, each side of the cube measures 4 inches. This is derived from the volume formula V = s 3 .
;
