2 Answers

Julien Lachal · Answer 1 · 2021-10-26T11:13:46+0000

We have been an image of a triangular pyramid. We are asked to find the volume of the given pyramid.

We know that volume of triangular pyramid is
$(1)/(3)b\cdot h$ , where,

b = Base area,

h = Height of pyramid.

We can see that base of pyramid a right triangle.

$\text{Area of triangle}=(1)/(2)*\text{Base}*\text{Height}$

Now we will find height of base triangle using Pythagoras theorem.

h^2=30^2-24^2

h^2=900-576

h^2=324

√(h^2)=√(324)

h=18

$\text{Area of base triangle}=(1)/(2)*24* 18$

$\text{Area of base triangle}=12* 18$

$\text{Area of base triangle}=216$

$\text{Volume of triangular prism}=(1)/(3)b\cdot h$

$\text{Volume of triangular prism}=(1)/(3)\cdot 216\cdot 30$

$\text{Volume of triangular prism}=216\cdot 10$

$\text{Volume of triangular prism}=2160$

Therefore, the volume of the given prism is
$2160\text{ m}^3$ and option B is the correct choice.

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