Question

b. solve for ( a ) when ( b = 11.03 mathrm{cm}, h = 14.17 mathrm{cm}, c = 20.15 mathrm{cm} ), and ( v = 1630 mathrm{cm}^{3} ). round the answer to 4 significant digits.
figure 15 - 15
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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: Write the volume formula for the wedge

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

Step2: Rearrange the formula to solve for \(a\)

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

Step3: Substitute the given values into the formula

Substitute \(V = 1630\space cm^{3}\), \(b = 11.03\space cm\), \(h = 14.17\space cm\), and \(c = 20.15\space cm\) into the formula:

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Answer:

\(a = 0.7100\space cm\)