The total cost to fill Kenny's entire attic given the cost per cubic yards is $904.50; option A
Triangular prism
- Cost of insulation = $16.75 per cubic yard
[tex]V = 1/4h \sqrt{ { - a}^{4} + 2 {ab}^{2} } + 2 {ac}^{2} - {b}^{4} + 2 {bc}^{2} - {c}^{4} [/tex]
= 1/4×9 √-4⁴ + 2(4×5)² + 2(4×3)² - 5⁴ + 2(5×3)² - 3⁴
= 9/4√256 + 2(20)² + 2(12)² - 3125 + 2(15)²- 81
= 9/4√256 + 2(400) + 3(144) - 3125 + 2(225) - 81
= 9/4√256 + 800 + 432 - 3125 + 450 - 81
= 9/4√-1268
= 54 cubic yard
Total cost to fill Kenny's entire attic = 54 × $16.75
= $904.50
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