Chapter 0.4, Problem 7E

(a)

To determine

To make: a table showing the number of cubes

Answer to Problem 7E

Figure no.	1	2	3
No. of cubes	8	12	16

Explanation of Solution

Given:

  

Calculation:

From the figures above, the number of cubes can be counted in each figure.

Cubes in figure 1 = 8

Cubes in figure 2 = 12

Cubes in figure 3 = 16

The following TABLE is the solution

Figure no.	1	2	3
No. of cubes	8	12	16

Conclusion:

Therefore, a table showing the number of cubes is drawn.

(b)

To determine

To write: a rule for the number of cubes

Answer to Problem 7E

The rule will be $8+\left(n-1\right)4$

Explanation of Solution

As we progress to next figure, 4 cubes are added to previous one

Since, we start with 8 cubes and add 4 on every next.

Number of cubes in nth figure $=8+\left(n-1\right)4$

Thus, using above rule,

Cubes in figure $1=8+0\times 4=8$

Cubes in figure $2=8+1\times 4=12$

Cubes in figure $3=8+2\times 4=16$

Conclusion:

Therefore, the rule will be $8+\left(n-1\right)4$

(c)

To determine

To write: the number of cubesin the tenth figure

Answer to Problem 7E

Here, ${10}^{th}$ figure will have 40 cubes.

Explanation of Solution

Building upon rule obtained in previous part, we find that,

Cubes in ${10}^{th}$ figure are $=8+\left(10-1\right)\cdot 4=8+32=40$

Thus, ${10}^{th}$ figure will have 40 cubes.

Conclusion:

Thus, ${10}^{th}$ figure will have 40 cubes.