Sold Menuration- Frustum of a rectangular pyramid

2 posts / 0 new
Last post
Harvey Biñan Lao
Harvey Biñan Lao's picture
Sold Menuration- Frustum of a rectangular pyramid

the height of a storage bin, in the form of a frustum of a rectangular pyramid, is 6 ft. its volume is 818cu.ft , and the upper base is 4 ft. by 16 ft. what are the dimensions of the lower base?

Jhun Vert
Jhun Vert's picture

$V = \frac{1}{3}(A_1 + A_2 + \sqrt{A_1A_2})h$

$818 = \frac{1}{3}\left[ \, 4(16) + A_2 + \sqrt{4(16)A_2} \, \right](6)$

$345 - A_2 = \sqrt{64A_2}$

$(345 - A_2)^2 = 64A_2$

$119,025 - 690A_2 + {A_2}^2 = 64A_2$

${A_2}^2 - 754A_2 + 119,025 = 0$

$A_2 = 529 ~ \text{and} ~ 225$
 

If A2 = 529, V = 1554 (not okay)
If A2 = 225, V = 818 (okay!)

Use A2 = 225 ft2
 

The lower base is proportional to the upper base

$\dfrac{a^2}{4^2} = \dfrac{225}{64}$

$a = 7.5 ~ \text{ft}$
 

$\dfrac{b^2}{16^2} = \dfrac{225}{64}$

$b = 30 ~ \text{ft}$
 

Dimensions = 7.5 ft × 30 ft           answer

Add new comment

Deafult Input

  • Allowed HTML tags: <img> <em> <strong> <cite> <code> <ul> <ol> <li> <dl> <dt> <dd> <sub> <sup> <blockquote> <ins> <del> <div>
  • Web page addresses and e-mail addresses turn into links automatically.
  • Lines and paragraphs break automatically.
  • Mathematics inside the configured delimiters is rendered by MathJax. The default math delimiters are $$...$$ and \[...\] for displayed mathematics, and $...$ and \(...\) for in-line mathematics.

Plain text

  • No HTML tags allowed.
  • Lines and paragraphs break automatically.