The three co-terminus edges of a rectangular solid are 36 cm, 75 cm and 80 cm respectively . Find the edge of a cube which will be of the same capacity :

Options

A. 60 cm
B. 52 cm
C. 46 cm
D. none of these

Answer

To find the edge of a cube that has the same capacity as a rectangular solid with edges 36 cm, 75 cm, and 80 cm, we need to follow these steps:

### Step 1: Calculate the Volume of the Rectangular Solid
The volume \( V \) of a rectangular solid (cuboid) is calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
In this case, the dimensions are 36 cm, 75 cm, and 80 cm. Therefore:
\[ V = 36 \, \text{cm} \times 75 \, \text{cm} \times 80 \, \text{cm} \]

### Step 2: Perform the Multiplication
Now, we will multiply these dimensions step by step:
1. First, multiply 36 cm and 75 cm:
\[ 36 \times 75 = 2700 \, \text{cm}^2 \]
2. Next, multiply the result by 80 cm:
\[ 2700 \, \text{cm}^2 \times 80 \, \text{cm} = 216000 \, \text{cm}^3 \]

### Step 3: Set the Volume of the Cube Equal to the Volume of the Rectangular Solid
Let \( a \) be the edge length of the cube. The volume \( V \) of a cube is given by:
\[ V = a^3 \]
Setting the volume of the cube equal to the volume of the rectangular solid:
\[ a^3 = 216000 \, \text{cm}^3 \]

### Step 4: Solve for \( a \)
To find \( a \), we take the cube root of both sides:
\[ a = \sqrt[3]{216000} \]

### Step 5: Calculate the Cube Root
To calculate \( a \):
1. Factor 216000:
\[ 216000 = 216 \times 1000 = 6^3 \times 10^3 \]
2. Therefore:
\[ a = \sqrt[3]{6^3 \times 10^3} = 6 \times 10 = 60 \, \text{cm} \]

### Conclusion
The edge of the cube that has the same capacity as the rectangular solid is:
\[ \boxed{60 \, \text{cm}} \]