To calculate the volume of the shape given a height and a base edge length, we need additional information about the shape, such as whether it's a prism or a pyramid. Assuming it is a rectangular prism with the height given as 12 m and one base edge measuring 6 m, we can denote the other edge of the base as \( b \).
The volume \( V \) of a rectangular prism is given by the formula:
\[ V = \text{Base Area} \times \text{Height} \] \[ V = ( \text{Base Edge 1} \times \text{Base Edge 2} ) \times \text{Height} \] \[ V = (6 , \text{m} \times b) \times 12 , \text{m} \]
Without the value of \( b \), we can't provide a specific answer for the volume until we know the area of the base. If we assume it's a square base and both edges are equal to 6 m:
\[ V = (6 \times 6) \times 12 = 36 \times 12 = 432 , \text{m}^3 \]
Now, to find the height given a volume of 48 units\(^3\) and a base edge length of 4 units, we use the same volume formula. Assuming again that it's a rectangular base (let's denote the other edge of the base as \( b \)), then:
\[ V = (4 \times b) \times h \]
Given that \( V = 48 , \text{units}^3 \):
\[ 48 = (4 \times b) \times h \]
To find \( h \), we need to find \( b \). If we assume \( b \) is also 4 units for a square base:
\[ 48 = (4 \times 4) \times h \] \[ 48 = 16 \times h \] \[ h = \frac{48}{16} = 3 , \text{units} \]
So the answers are:
- For the volume with height 12 m and base edge 6 m, if it is a square base: \( V = 432 , \text{m}^3\) (with another base edge of 6 m).
- For the height where volume is 48 units³ and one base edge is 4 units (assuming a square base): \( h = 3 , \text{units} \).