The base of a triangular pyramid is a triangle with corners at $(4, 1)$ $(4 ,1 )$ , $(3, 1)$ $(3 ,1 )$ , and $(9, 5)$ $(9 ,5 )$ . If the pyramid has a height of $8$ $8$ , what is the pyramid's volume?

Question

The base of a triangular pyramid is a triangle with corners at $(4, 1)$ $(4 ,1 )$ , $(3, 1)$ $(3 ,1 )$ , and $(9, 5)$ $(9 ,5 )$ . If the pyramid has a height of $8$ $8$ , what is the pyramid's volume?

1 Answer

Impact of this question

1252 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-31T01:56:15

$\frac{16}{3} = 5.33$ $16/3=5.33$

Explanation:

enter image source here

Pyramid volume $V = \frac{1}{3} \cdot A \cdot H$ $V=1/3*A*H$ , where $A$ $A$ is the pyramid's base area and $H$ $H$ is the height of the pyramid.

Given that $A (3, 1), B (4, 1) and C ((, 5)$ $A(3,1), B(4,1) and C((,5)$ are the triangular base's corners, as shown in the diagram,
$\Rightarrow A = \frac{1}{2} \cdot 1 \cdot 4 = 2$ $=> A=1/2*1*4=2$

Given that the pyramid has a height of $8, \Rightarrow H = 8$ $8, => H=8$

$\Rightarrow V = \frac{1}{3} A H = \frac{1}{3} \cdot 2 \cdot 8 = \frac{16}{3} = 5.33$ $=> V=1/3AH=1/3*2*8=16/3=5.33$

Science

Math

Humanities

... and beyond

The base of a triangular pyramid is a triangle with corners at $(4, 1)$ $(4 ,1 )$ , $(3, 1)$ $(3 ,1 )$ , and $(9, 5)$ $(9 ,5 )$ . If the pyramid has a height of $8$ $8$ , what is the pyramid's volume?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

The base of a triangular pyramid is a triangle with corners at (4 ,1 )(4,1)(4 ,1 ), (3 ,1 )(3,1)(3 ,1 ), and (9 ,5 )(9,5)(9 ,5 ). If the pyramid has a height of 8 88 , what is the pyramid's volume?

1 Answer

Explanation:

Related questions

Impact of this question

The base of a triangular pyramid is a triangle with corners at $(4, 1)$ $(4 ,1 )$ , $(3, 1)$ $(3 ,1 )$ , and $(9, 5)$ $(9 ,5 )$ . If the pyramid has a height of $8$ $8$ , what is the pyramid's volume?