If the volume of a cube is $3375 cm^3$, find its height and area of the base.
Answer (2)
Find the side length of the cube by taking the cube root of the volume: s = 3 3375 = 15 c m .
Determine the height of the cube, which is equal to the side length: h = s = 15 c m .
Calculate the area of the base by squaring the side length: A = s 2 = 1 5 2 = 225 c m 2 .
State the height and base area: 15 c m and 225 c m 2 .
Explanation
Problem Analysis We are given that the volume of a cube is 3375 c m 3 . We need to find the height and the area of the base of the cube.
Formulas Let V be the volume of the cube, h be its height, and A be the area of its base. Since it is a cube, all sides are equal, so the height is equal to the side length, h = s . The volume of a cube is given by V = s 3 , where s is the side length. The area of the base of the cube is given by A = s 2 .
Calculate Side Length First, we need to find the side length s of the cube. Since V = s 3 , we have s = 3 V = 3 3375 . The result of the cube root is s = 15 c m .
Determine Height Since the height is equal to the side length, the height of the cube is h = s = 15 c m .
Calculate Base Area Now, we need to find the area of the base of the cube. The area of the base is given by A = s 2 . Substituting s = 15 c m , we get A = ( 15 c m ) 2 = 225 c m 2 .
Final Answer Therefore, the height of the cube is 15 c m and the area of the base is 225 c m 2 .
Examples
Cubes are common in everyday life, from sugar cubes to dice. Knowing how to calculate the height and base area from the volume is useful in various applications. For example, if you're designing a cubic storage container and know the desired volume, you can determine the necessary dimensions and the material needed for the base. If you want a volume of 3375 c m 3 , then the side of the cube should be 15 c m . The area of the base will be 225 c m 2 .
The height of the cube is 15 cm and the area of the base is 225 cm². Both calculations are based on the cube's volume of 3375 cm³. The side length is determined first by taking the cube root of the volume, and then used to find the area of the base.
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