To determine the height of a rectangular solid with the given volume, length, and breadth, we'll follow these steps:
1. Understand the formula for the volume of a rectangular solid:
The volume ([tex]\( V \)[/tex]) of a rectangular solid can be calculated using the formula:
[tex]\[
V = \text{length} \times \text{breadth} \times \text{height}
\][/tex]
2. Identify the known values:
- Volume ([tex]\( V \)[/tex]) = 280 cm³
- Length ([tex]\( l \)[/tex]) = 8 cm
- Breadth ([tex]\( b \)[/tex]) = 7 cm
3. Rearrange the formula to solve for the height ([tex]\( h \)[/tex]):
To find the height, we rearrange the volume formula:
[tex]\[
h = \frac{V}{l \times b}
\][/tex]
4. Substitute the known values into the rearranged formula:
[tex]\[
h = \frac{280}{8 \times 7}
\][/tex]
5. Calculate the height:
First, calculate the denominator:
[tex]\[
8 \times 7 = 56
\][/tex]
Next, divide the volume by the product of the length and breadth:
[tex]\[
h = \frac{280}{56} = 5
\][/tex]
Therefore, the height of the rectangular solid is [tex]\( 5 \)[/tex] cm.
The answer is:
A 5 cm
