The formula for finding the volume of a pyramid is [tex]v=b h / 3[/tex]. What formula should you use to find the altitude [tex]h[/tex]?
A. [tex]h=3 b / v[/tex]
B. [tex]h=v / 3 b[/tex]
C. [tex]h=3 b v[/tex]
D. [tex]h=3 v / b[/tex]
Answer (2)
Start with the volume formula: v = 3 bh .
Multiply both sides by 3: 3 v = bh .
Divide both sides by b to isolate h : h = b 3 v .
The correct formula for the altitude is h = b 3 v .
Explanation
Understanding the Formula We are given the formula for the volume of a pyramid: v = 3 bh , where v is the volume, b is the base area, and h is the altitude (height). We need to find the formula for h in terms of v and b .
Multiplying by 3 To isolate h , we need to get rid of the fraction and the b on the right side of the equation. First, let's multiply both sides of the equation by 3: 3 × v = 3 × 3 bh 3 v = bh
Dividing by b Now, to isolate h , we divide both sides of the equation by b : b 3 v = b bh b 3 v = h So, h = b 3 v .
Finding the Correct Option The formula for the altitude h is h = b 3 v . Comparing this with the given options, we see that option D matches our result.
Examples
Understanding how to rearrange formulas like the volume of a pyramid is useful in many real-world scenarios. For example, if you're an architect designing a pyramid-shaped building and you know the desired volume and base area, you can use this rearranged formula to calculate the necessary height of the structure. Similarly, if you're working on a construction project and need to determine the height of a pile of material shaped like a pyramid, knowing the volume and base area allows you to quickly find the height.
To find the altitude h of a pyramid, rearrange the volume formula v = 3 bh to get h = b 3 v . The correct option is D. This formula allows you to calculate the height when the volume and base area are known.
;
