Question

b. solve for a when b = 11.03 cm, h = 14.17 cm, c = 20.15 cm and v = 1630 cm³. round the answer to 4 significant digits. figure 15 - 15 details the distance between the base and the top length, c of the wedge = h. the base length is a, and the base width is b.

Explanation:

Step1: Recall volume formula

The volume formula for the given wedge - shaped solid is $V=\frac{1}{2}(a + c)bh$.

Step2: Rearrange formula for $a$

First, multiply both sides of the formula by $2$ to get $2V=(a + c)bh$. Then divide both sides by $bh$: $\frac{2V}{bh}=a + c$. Finally, solve for $a$: $a=\frac{2V}{bh}-c$.

Step3: Substitute given values

Substitute $V = 1630\ cm^{3}$, $b = 11.03\ cm$, $h = 14.17\ cm$, and $c = 20.15\ cm$ into the formula for $a$.
$a=\frac{2\times1630}{11.03\times14.17}-20.15$.
First, calculate the denominator $11.03\times14.17 = 11.03\times(14 + 0.17)=11.03\times14+11.03\times0.17=154.42+1.8751 = 156.2951$.
Then, $2\times1630 = 3260$. So, $\frac{3260}{156.2951}\approx20.86$.
Finally, $a=20.86 - 20.15=0.7100\ cm$.

Answer:

$0.7100\ cm$