Question

The Sahara Desert has an area of approximately 9 400 000 km^2. While estimates of its average depth vary, they center around 150 m. One cm^3 holds approximately 8 000 grains of sand. a. Approximately how many grains of sand are in the Sahara Desert? b. What fraction of the Sahara is made by 1 grain of sand? c. A small dump truck can carry approximately 20.5 m^3 of sand. Suppose a long line of dump trucks were to dump a load of sand every 30 seconds. How many years would it take to re-create the Sahara Desert?

Answer 1

Answer:

a). $1.128\times 10^{25}$ grains

b). $\frac{1}{8000}$

c). $6.54305\times 10^{7}$ years

Step-by-step explanation:

a). Given Sahara desert has an area of approximately = 9400000 km²

= 9400000×(10000000000) cm²

= $9.4\times 10^{16}$ cm²

Depth of the desert = 150 m

= 15000 cm

Volume of desert = Area × Depth

= $9.4\times 10^{16}\times 15000$

= $1.41\times 10^{21}$ cm³

Since 1 cm³ holds sand grains = 8000

Therefore, Grains in Sahara Desert = $1.41\times 10^{21}\times 8000$

= $1.128\times 10^{25}$

b). Since 1 cm³ = 8000 grains

1 grain = $\frac{1}{8000}$ cm³

c). A truck can carry sand = 20.5 m³ Or $20.5\times (10^{2})^{3} cm^{3}$

= $2.05\times 10^{7}$ cm³

Now time taken to recreate Sahara Desert = $\frac{\text{Total amount of sand}}{\text{Sand in one truck}}\times 30$ seconds

=  $\frac{1.41\times 10^{21}}{2.05\times 10^{7}}\times 30$

= $20.6341463\times 10^{14}$ seconds

= $\frac{20.6341463\times 10^{14} }{365\times \times 24\times 3600}$ years

= $6.54305\times 10^{7}$ years