A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the pyramid is 210 cubic units, what is the volume of the prism?

(1 point)
Responses

210 cubic units
210 cubic units

630 cubic units
630 cubic units

1,260 cubic units
1,260 cubic units

70 cubic units

1 answer

The volume of a pyramid is given by the formula:

\[ V_{\text{pyramid}} = \frac{1}{3} \times B \times h \]

where \( B \) is the area of the base and \( h \) is the height.

Given that the volume of the pyramid is 210 cubic units, we can express the area of the base and height in terms of this volume:

\[ 210 = \frac{1}{3} \times B \times h \]

To find the volume of the prism, we use the formula for the volume of a prism:

\[ V_{\text{prism}} = B \times h \]

Now, we can relate the volumes of the pyramid and prism. From the pyramid's volume formula:

\[ B \times h = 3 \times 210 = 630 \text{ cubic units} \]

Thus, the volume of the prism is 630 cubic units.

So, the answer is:

630 cubic units.