Math Problem Statement

The volume of a cubical box is 24,60,375 cm³. Find the length of its side.

Solution

The image shows a math problem regarding the volume of a cubical box. The problem asks to find the length of its side, given that the volume is 24,60,375 cm³.

The formula for the volume of a cube is:

Volume=side3\text{Volume} = \text{side}^3

Given: Volume=24,60,375cm3\text{Volume} = 24,60,375 \, \text{cm}^3

To find the side length, we need to take the cube root of the volume:

side=24,60,3753\text{side} = \sqrt[3]{24,60,375}

I will calculate this for you.The length of the side of the cubical box is approximately 135 cm.

Would you like more details on how this was solved? Here are some related questions for practice:

  1. If the volume was 1,728 cm³, what would the side length be?
  2. How does the volume change if the side length is doubled?
  3. What is the surface area of a cube with a side length of 135 cm?
  4. Can you find the diagonal of a cube with a side length of 135 cm?
  5. If the volume of a cubical box is reduced to half, what will be the new side length?

Tip: When calculating cube roots of large numbers, rounding might slightly affect precision. Always consider the context of the problem!

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Math Problem Analysis

Mathematical Concepts

Geometry
Cubic Volume
Roots

Formulas

Volume of cube = side^3
side = cube root of Volume

Theorems

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Suitable Grade Level

Grades 6-8