If the volume of a cube is 175616 cm 3, what is its side?
56 cm
Calculating the Side Length of a Cube from its Volume
The question asks us to find the side length of a cube when its volume is given as 175616 cm3.
Understanding Cube Volume
A cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. All 12 of the cube's edges are of equal length, and all 8 of the vertices are of equal angle.
The volume of a cube is the amount of space it occupies. It is calculated by multiplying the length of one side by itself three times.
Formula for Cube Volume
If 's' represents the length of one side of the cube, the volume 'V' of the cube is given by the formula:
\( V = s^3 \)
Finding the Side Length
To find the side length 's' when the volume 'V' is known, we need to calculate the cube root of the volume. The cube root operation is the inverse of cubing a number.
The formula to find the side length 's' is:
\( s = \sqrt[3]{V} \)
Step-by-Step Calculation
Given the volume \( V = 175616 \) cm3, we need to find the side length 's'.
Using the formula \( s = \sqrt[3]{V} \), we substitute the given volume:
\( s = \sqrt[3]{175616} \)
We need to find a number that, when multiplied by itself three times, equals 175616.
Let's test the options provided:
- Option 1: 36 cm. \( 36^3 = 36 \times 36 \times 36 = 1296 \times 36 = 46656 \)
- Option 2: 66 cm. \( 66^3 = 66 \times 66 \times 66 = 4356 \times 66 = 287496 \)
- Option 3: 46 cm. \( 46^3 = 46 \times 46 \times 46 = 2116 \times 46 = 97336 \)
- Option 4: 56 cm. \( 56^3 = 56 \times 56 \times 56 = 3136 \times 56 = 175616 \)
From the calculations, we see that \( 56^3 = 175616 \).
Therefore, the side length of the cube is 56 cm.
\( s = 56 \text{ cm} \)
Summary of Solution
Given Volume \( V = 175616 \) cm3.
Side length \( s = \sqrt[3]{V} \).
\( s = \sqrt[3]{175616} \)
\( s = 56 \) cm.
| Given | Formula | Calculation | Result |
|---|---|---|---|
| Volume = 175616 cm3 | \( V = s^3 \implies s = \sqrt[3]{V} \) | \( s = \sqrt[3]{175616} \) | s = 56 cm |
Revision Table: Cube Properties
| Property | Formula (Side 's') |
|---|---|
| Volume (V) | \( s^3 \) |
| Surface Area (A) | \( 6s^2 \) |
| Face Diagonal (df) | \( s\sqrt{2} \) |
| Space Diagonal (ds) | \( s\sqrt{3} \) |
Additional Information: Cube Roots
Finding the cube root of a number is like asking what number was multiplied by itself three times to get the original number.
- For example, the cube root of 8 is 2 because \( 2 \times 2 \times 2 = 8 \).
- The cube root of 27 is 3 because \( 3 \times 3 \times 3 = 27 \).
In this problem, we were looking for the number whose cube is 175616, which we found to be 56.
Important Questions from Solid Figures
The area of the floor of a cubical room is 192 m 2. The length of the longest rod that can be kept in that room is :
A solid metallic rectangular block of dimensions 112 cm × 44 cm × 25 cm is melted and recast into a cylinder of radius 35 cm. The curved surface area (in cm 2) of the cylinder is: (Take π = 22/7)
The volume of a right circular cone is 1232 cm 3. If the height of the cone is 24 cm, then what will be the radius of its base?
A right triangle contains the right angle between the sides 5 cm and 7 cm. A cone is generated by revolving about the side 5 cm. The volume of this cone is:
The area of the base of a right circular cone is \(\frac{1408}{7} cm^2\) and its height is 6 cm. Taking π = \(\frac{22}{7}\) , the curved surface area of the cone is:
