Measuring 67734

The candle has the shape of a block measuring 3 cm, 4 cm, and 5 cm. How many times is more wax used to make a candle if we gradually enlarge one, two, and all three edges twice?

Correct answer:

n =  64

Step-by-step explanation:

$$\begin{gathered} a_1=3\text{cm} \\ {b}_1=4\text{cm} \\ {c}_1=5\text{cm} \\ {a}_2=2\cdot a_1=2\cdot 3=6\text{cm} \\ {b}_2=b_1=4\text{cm} \\ {c}_2=c_1=5\text{cm} \\ {a}_3=2\cdot a_2=2\cdot 6=12\text{cm} \\ {b}_3=2\cdot b_2=2\cdot 4=8\text{cm} \\ {c}_3=c_2=5\text{cm} \\ {a}_4=2\cdot a_3=2\cdot 12=24\text{cm} \\ {b}_4=2\cdot b_3=2\cdot 8=16\text{cm} \\ {c}_4=2\cdot c_3=2\cdot 5=10\text{cm} \\ {V}_1=a_1\cdot b_1\cdot c_1=3\cdot 4\cdot 5=60{\text{cm}}^3 \\ {V}_2=a_4\cdot b_4\cdot c_4=24\cdot 16\cdot 10=3840{\text{cm}}^3 \\ n=V_2/V_1=3840/60=64 \\ \text{ Verifying Solution: } \\ {n}_1=2^6=64 \end{gathered}$$

Try another example