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leonid [27]
3 years ago
6

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?
Mathematics
1 answer:
Andrew [12]3 years ago
6 0

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

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