Answer:
a) To find the time it will take William to cover the path shown on the map, we need to convert the length of the path from centimeters to kilometers using the map scale. 1 cm on the map represents 40,000 cm in reality, which is equivalent to 0.4 km. So, the length of the path in kilometers is:
36 cm x 0.4 km/cm = 14.4 km
Now we can use the formula time = distance ÷ speed to find how long it will take William to cover the path:
time = distance ÷ speed = 14.4 km ÷ 5 km/h = 2.88 hours or 2 hours and 52.5 minutes (rounded to the nearest minute).
b) The area of the rectangular field can be found by multiplying its dimensions together, then converting the area from square centimeters to hectares using the scale of the map.
Area of field = 9 cm x 7 cm = 63 cm²
Area of field in hectares = 63 cm² ÷ (20,000 cm/ha)² = 0.0001575 ha
To find how many tons of barley the farmer needs, we can use the given conversion factor of 0.3 tons of barley per hectare:
Tons of barley needed = 0.0001575 ha x 0.3 tons/ha = 0.00004725 tons or 47.25 grams of barley.
c) To find the area of the pool in reality, we need to convert the area of the pool on the map from square centimeters to square meters using the map scale.
Area of pool on map = 18.84 cm²
Area of pool in reality = 18.84 cm² x (500 cm/m)² = 0.471 m²
d)
1) The length of the straight edge of the figure can be found using the Pythagorean theorem:
a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
c = √25 = 5 cm
The area of the figure can be found by adding the area of the triangle and the semicircle:
Area of triangle = 1/2 x base x height = 1/2 x 3 cm x 4 cm = 6 cm²
Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5/2)² = 19.63 cm²
Total area of figure = 6 cm² + 19.63 cm² = 25.63 cm²
2) To draw the figure on a scale of 1:2, we need to multiply all dimensions by 2. So, the straight edge of the figure would be 10 cm long, the base of the triangle would be 6 cm, and the height of the triangle would be 8 cm. The radius of the semicircle would be 5 cm.
Using the same calculations as before, we can find the area of the figure on the new scale:
Area of triangle = 1/2 x base x height = 1/2 x 6 cm x 8 cm = 24 cm²
Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5 cm)² = 39.27 cm²
Total area of figure = 24 cm² + 39.27 cm² = 63.27 cm²
3) To find the length and area of the figure twice its original size, we need to multiply all dimensions by 2. So, the straight edge of the figure would be 10 cm long, the base of the triangle would be 6 cm, and the height of the triangle would be 8 cm. The radius of the semicircle would be 5 cm.
Using the same calculations as before, we can find the area of the figure on the new scale:
Area of triangle = 1/2 x base x height = 1/2 x 6 cm x 8 cm = 24 cm²
Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5 cm)² = 39.27 cm²
Total area of figure = 24 cm² + 39.27 cm² = 63.27 cm²
e) Without knowing the specific proportion, it's difficult to provide a solution. Please provide more information or the specific proportion so that we can help you solve it.