Question

Valeria created a triangular pyramid as part of her science fair project. The triangular base has a height of 8 cm and a length of 6 cm. The height of the pyramid is 12 cm. Determine the volume of Valeria's pyramid.A. 192 cm B. 288 cmC. 96 cmD. 576 cm

Answer 1

Given:

Height of triangular base = 8 cm

Length of traingular base = 6cm

Height of pyramid = 12 cm

Let's determine the volume of Valeria's pyramid.

To find the volume of the triangular pyramid, apply the formula:

`V=(1)/(3)(A\ast h)`

Where A is the area of the triangular base and h is the height of the pyramid

To find the area of the triangular base, apply the area of a triangle formula:

`\begin{gathered} A=(b\ast h)/(2) \\ \\ A=\frac{6\ast8^{}}{2}=(48)/(2)=24cm^2 \end{gathered}`

To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.

Thus, we have:

`\begin{gathered} V=(1)/(3)(A\ast h) \\ \\ V=(1)/(3)(24\ast12) \end{gathered}`

Solving further:

`\begin{gathered} V=(1)/(3)(288) \\ \\ V=(288)/(3) \\ \\ \text{ V = 96 cm}^3 \end{gathered}`

Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.

ANSWER:

`\text{ C. 96 cm}^3`