Question

9-42 A. Examine the 1 × 1 × 3 solid below.B. If this shape is enlarged by a linear scale factor of 2, how wide will the new shape be? How tall? How deep?C. How many of the 1 × 1 × 3 solids would you need to build the enlargement described in part (b) above? Use blocks to prove your answer.D. What if the 1 × 1 × 3 solid is enlarged with a linear scale factor of 3? How many times larger would the volume of the new solid be? Explain how you found your answer.

Answer 1

(A). We are given a 1 x 1 x 3 solid.

(B). If it is enlarged by a scale factor of 2, The new dimension will be 2 x 2 x 6

(C). Here we will find the surface Area of the New divided by the surface area of the former

The number (n) needed is

`\begin{gathered} n=(2\left(LB+LH+BH\right))/(2\left(lb+lh+bh\right?) \\ n=(LB+LH+BH)/(lb+lh+bh) \\ n=(2\left(2\right)+2\left(6\right)+2\left(6\right))/(1\left(1\right)+1\left(3\right)+1\left(3\right)) \\ n=(4+12+12)/(1+3+3) \\ n=(28)/(7) \\ n=4 \end{gathered}`

Therefore, four 1 x 1 x 3 solids would be needed

(D).

Scale factor = 3

`Volume=3^3=27`

The volume would be 27 times larger