QuestionFind the actual area of a park (8 cm² on a 1:25000 map) in m², expressed in scientific notation.

Studdy Solution

STEP 1

Assumptions1. The scale of the map is125000, meaning1 cm on the map represents25000 cm in reality. . The area of the park on the map is8 cm².
3. We need to find the actual area of the park in m². 4.1 m =100 cm.

STEP 2

First, we need to find the actual length and width of the park. Since the area of the park on the map is a square, we can take the square root of the area to find the length of one side.
$\text{Side length on map} = \sqrt{\text{Area on map}}$

STEP 3

Now, plug in the given value for the area on the map to calculate the side length on the map.
$\text{Side length on map} = \sqrt{8 \, \text{cm}^2}$

STEP 4

Calculate the side length on the map.
$\text{Side length on map} = \sqrt{8} \, \text{cm} =2.83 \, \text{cm}$

STEP 5

Now that we have the side length on the map, we can find the actual side length in reality by multiplying the side length on the map by the scale.
$\text{Actual side length} = \text{Side length on map} \times \text{Scale}$

STEP 6

Plug in the values for the side length on the map and the scale to calculate the actual side length.
$\text{Actual side length} =2.83 \, \text{cm} \times25000$

STEP 7

Calculate the actual side length.
$\text{Actual side length} =2.83 \, \text{cm} \times25000 =70750 \, \text{cm}$

STEP 8

Now that we have the actual side length in cm, we can convert this to meters by dividing by100.
$\text{Actual side length in m} = \text{Actual side length in cm} /100$

STEP 9

Plug in the value for the actual side length in cm to calculate the actual side length in m.
$\text{Actual side length in m} =70750 \, \text{cm} /100$

STEP 10

Calculate the actual side length in m.
$\text{Actual side length in m} =70750 /100 =707.5 \, \text{m}$

STEP 11

Now that we have the actual side length in m, we can find the actual area of the park by squaring the side length.
\text{Actual area} = (\text{Actual side length in m})^

STEP 12

Plug in the value for the actual side length in m to calculate the actual area.
$\text{Actual area} = (707.5 \, \text{m})^2$

STEP 13

Calculate the actual area.
$\text{Actual area} = (707.5)^2 =500062.5 \, \text{m}^2$

STEP 14

Now that we have the actual area, we can express this in scientific notation.
\text{Actual area in scientific notation} =.000625 \times10^ \, \text{m}^2The actual area of the park is .000625 \times10^ \, \text{m}^2.

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