Chapter 12.5, Problem 20HP

To determine

To find: whether S or R is finding the correct surface area of the cube

Answer to Problem 20HP

The calculation of R is correct.

Explanation of Solution

Given:

S	R
$2\cdot 2\cdot 2=8c{m}^3$	$8\cdot 2+2\cdot 2\cdot 2=24c{m}^3$

  

Calculation:

Consider the side of the cube is 2 cm.

The objective is to find which calculation is correct.

The volume V of the cube is #.

Here, a is the side of the cube.

As a = 2

Thus,

  $\begin{array}{c}V=2\cdot 2\cdot 2\\ =8{\text{cm}}^2\end{array}$

Hence, the calculation of S is the volume not the surface area. Hence the calculation is in correct.

The lateral area L of a square prism is, $L=P\cdot h$ .

Here, P is the perimeter of the base and h is the height the square prism.

The surface area S of a square prism is, S = L + 2B.

Here, L is the lateral area and B is the area of the base.

The base of the prism is a square whose side is l .

The perimeter P of the base of the prism is, P = 4l .

Here, l is the side of the square base.

Substitute P = 4l and h = l in the lateral area formula to find the lateral area of the prism.

Thus,

  $\begin{array}{c}L=P\cdot h\\ =4\cdot 2\cdot 2\\ =8\cdot 2\end{array}$

Therefore, the lateral area of the square prism is $8\cdot 2{\text{cm}}^2$ .

Find the surface area of the square prism.

The area B of the base of the prism is.

  $\begin{array}{c}B=2^2\\ =2\cdot 2\end{array}$

Substitute $B=2\cdot 2$ and $L=8\cdot 2$ in the surface area formula to find the surface area of the prism

  $\begin{array}{c}S=L+2B\\ =8\cdot 2+2\cdot 2\cdot 2\\ =24{\text{cm}}^2\end{array}$

Conclusion:

Hence, the calculation of R is correct.