Chapter 12.5, Problem 28HP

To determine

To find: complete the volume of the prism, and explain reasoning.

Answer to Problem 28HP

Both rectangular prisms have same volume.

Explanation of Solution

Given information: Two prisms are shown.

  

Formula used:

Volume of rectangle prism = $l\times w\times h$

Calculation:

Rectangular prism 1, dimensions are (8cm, 8cm, 8cm)

Rectangular prism 2, dimension are (8cm, 4cm, 16cm)

Now,

  $\begin{array}{l}volum{e}_1=8\times 8\times 8=512c{m}^3\\ volum{e}_2=8\times 4\times 16=512c{m}^3\end{array}$

Both shown rectangular prism have same volume.

In both shown prisms base is same,

Width of 1 prism is 8cm and in 2, it is half of 1 prism I.e. 4 cm.

Where as height of 1 prism is 8 cm and height of 2 prisms is twice height of first prism.

Therefore, half width of 2 prism of the first and twice height of 2 prism prism to the first, compensate.

Hence, both volumes are equal.

In rough sense, multiplying $8\times 8\times 8=512and8\times 4\times 16=512$

Volume will be same.