Calculate Cube Volume with 42m Edge
This solution explains how to find the volume of a cube when the length of its edge is known, using the provided details.
Understanding Cube Volume
A cube is a three-dimensional solid object with six equal square faces. All its edges have the same length. To calculate the volume of a cube, you only need to know the length of one edge.
Cube Volume Formula
The volume ($V$) of a cube is calculated by cubing the length of its edge ($s$). The formula is expressed in LaTeX as:
$$V = s^3$$
Here, '$V$' represents the volume and '$s$' represents the length of one edge of the cube.
Calculation Steps
The problem states that the length of each edge of the cube is 42 meters. Follow these steps to calculate the volume:
- Given Edge Length ($s$): The edge length is given as $s = 42 \, \text{m}$.
- Apply the Volume Formula: Substitute the edge length into the volume formula: $$V = (42 \, \text{m})^3$$
- Step 1: Calculate $42 \times 42$. $$42 \times 42 = 1764$$
- Step 2: Multiply the result by 42. $$1764 \times 42 = 74088$$
- Final Volume: The calculated volume of the cube is $74,088 \, \text{m}^3$.
Comparing with Provided Options
Let's compare the calculated volume with the options given in the question:
- Option 1: 74,236
- Option 2: 74,009
- Option 3: 74,283
- Option 4: 74,088
The computed volume $74,088 \, \text{m}^3$ exactly matches Option 4.
Conclusion
The volume of a cube with an edge length of 42 meters is $74,088 \, \text{m}^3$. This corresponds to the fourth option provided.
Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
Which of the following is a geometrical figure with a three-dimensional geometry that has eight vertices and six rectangular faces?
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
