Question

Extra Credit (a) Calculate the number of seconds in 4 years. (b) If 1 cm3 is the volume of a cube with each side having length 1 cm and a new cube is made having a length, width and height of 10 1 cm3 cubes, what is the volume of the new cube in m3?

Answer 1

(a) First let us consider an year. An year consists of normally 365 days (expect leap year having 366 days) each with 24 hours, each hour with 60 minutes and each minute 60 seconds.

Therefore, number of seconds in an year =

365 × 24 × 60 × 60 = 31536000 s

Therefore, 4 years contain 4 × 31536000 = 126144000 seconds.

But 4 years contain a leap year making 366 days in any of the 4 years. That is there will be an extra day.

1 day = 24 × 60 ×60 = 86400 seconds.

Therefore, the number of seconds in 4 years = 126144000 + 86400 = 126230400 seconds

(b) A $1\,\,cm^3$ cube has a length, width and height if 1cm.

(volume of the cube = $side^3=a^3=1^3=1 cm^3$ )

The new cube is made having a length, width and height of 10, $1 cm^3$ cubes.

Since,a $1 cm^3$ cube has sides of length 1cm, the new cube having 10 $1 cm^3$ cube on each side has a side length of 10 cm.(That is 10 cm length,10 cm width and 10 cm height).

Therefore the volume of the new cube

$=a^3=10^3=1000\,\, cm^3$

We know that 1 m = 100 cm

That makes, 1 cm = 1/100 = 0.01 = $10^-^2$ m

Now, $1 \,\, cm^3=(10^-^2)^3m^3=10^-^6\,\,m^3$

Therefore, the volume of the new cube = $1000\,\,cm^3=1000\times10^-^6\,\,m^3=10^-^3 \,\,m^3$