Question

A vineyard has 165 acres of chardonnay grapes. a particular soil supplement requires 6.00 grams for every square meter of vineyard. how many kilograms of the soil supplement are required for the entire vineyard? (recall that 1 km2 = 247 acres)

Answer 1

4008.10 kg

Explanation:

We have been given that a vineyard has 165 acres of chardonnay grapes. a particular soil supplement requires 6.00 grams for every square meter of vineyard.

We know that 1 squared km equals 247 acres.

`\text{165 acres}*\frac{\text{1 km}^2}{\text{247 acres}}`

`165*\frac{\text{1 km}^2}{247}`

`0.6680161943319838\text{ km}^2`

We know 1 square km equals 1000000 meters.

`0.6680161943319838\text{ km}^2* \frac{1000000\text{ m}^2}{\text{ km}^2}`

`0.6680161943319838* 1000000\text{ m}^2`

`668016.1943319838\text{ m}^2`

Now, we will multiply 6 by
`668016.1943319838\text{ m}^2`.

`668016.1943319838\text{ m}^2* \frac{\text{6 grams}}{\text{m}^2}`

`668016.1943319838* \text{6 grams}`

`4008097.1659919028\text{ grams}`

`4008097.1659919028\text{ grams}* \frac{1\text{ kg}}{\text{1000 grams}}`

`4008.09716599190281\text{ kg}`

`4008.10\text{ kg}`

Therefore, 4008.10 kg of the soil supplement are required for the entire vineyard.

Answer 2

1 km^2 = 1000m x 1000m = 1 x 10^6 m^2
(145 acres / 247 acres) x 1 x 10^6 m^2 = 5.87 x 10^5 m^2
5.5 g/m^2 x 5.87 x 10^5 m^2 = 3.23 x 10^6 g
3.23 x 10^6 g x 1kg/10000 g = 3.23 x 10^3 kg