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3 years ago

Work out the volume of the prism (answer in 1 decimal place)

Mathematics

1 answer:

Artyom0805 [142]3 years ago

4 0

Answer:

Volume of the Prism = $204 cm^3$

Step-by-step explanation:

Volume of the right triangular prism= $\frac{1}{2}*Length*Width*Height$

Length=8.5 cm

Width= 6 cm

Height= 8 cm

Putting the values in the formula:

Volume of the prism :

$\frac{1}{2}*8.5*6*8\\\\=\frac{1}{2}*8.5*48\\\\ =\frac{1}{2} *408\\\\=204cm^3$

The volume of the Prism is $204 cm^3$

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Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

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Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

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$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

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$8\, r^2 - 25\, r + 8 = 0$ .

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Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

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