Mathematics: A rectangular pyramid and a rectangular prism are shown below. If the volume of the pyramid is 12 ft3, what is the volume of the prism? Explain why and how you found your answer.

19Step-by-step explanation:12+27=3958-39...

A rectangular pyramid and a rectangular prism are

elijahcarson9015

21.01.2022

The volume of the rectangular prism is 36 ft³.

Step-by-step explanation:

Step 1:

The volume of a rectangular prism = lwh ,

The area of the base is length multiplied by the width. So Area = (l)(w).

The volume of a rectangular prism = (area)(h).

The volume of a rectangular pyramid $= a^{2} \frac{h}{3} .$

Where a is the side length. If the base is a square, the area $= a^{2}$ .

So the volume of a rectangular pyramid $=\frac{1}{3} (area)(h)$ .

So if a rectangular pyramid and a rectangular prism have the same base and height, then

3 times the volume of the rectangular pyramid = The volume of the rectangular prism.

Step 2:

As it is given that the volume of the pyramid is 12 ft³, we can calculate the volume of the prism. As both the shapes have the same height and base,

The volume of the prism = (12)(3) = 36.

The volume of the rectangular prism is 36 ft³.

0,0(0 оценок)