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Find the missing dimension of the prism. Round your answer to the nearest hundredth.

Volume = 72.66 in.?

Х

2 in.

Sagot :

MrRoyalidn

Answer:

[tex]x = 6.99in[/tex]

Step-by-step explanation:

Given

[tex]l =2in[/tex]

[tex]Volume = 72.66in^3[/tex]

See attachment for prism

Required

Find x

The prism has a regular hexagon base

The base area is calculated as:

[tex]Base\ Area= \frac{3\sqrt 3}{2}l^2[/tex]

This gives:

[tex]Base\ Area= \frac{3\sqrt 3}{2} * 2^2[/tex]

[tex]Base\ Area= \frac{3\sqrt 3}{2} * 4[/tex]

[tex]Base\ Area= 3\sqrt 3 * 2[/tex]

[tex]Base\ Area= 6\sqrt 3[/tex]

Side x represents the height.

So, we have:

[tex]Volume = Base\ Area*x[/tex]

Make x the subject

[tex]x = \frac{Volume }{ Base\ Area}[/tex]

[tex]x = \frac{72.66in^3}{6\sqrt 3 in^2}[/tex]

[tex]x = \frac{72.66}{6\sqrt 3}in[/tex]

[tex]x = \frac{12.11}{\sqrt 3}in[/tex]

[tex]x = 6.99in[/tex] --- approximated

View image MrRoyal
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