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A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.
- a)1655
- b)1665
Correct answer is between '1655,1665'. Can you explain this answer?
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A map has shrunk and the 15 cm reference line now measures 14 cm. If ...
Shrunk Scale = 14/15 x 1/30 = 1/32.1428
Volume = (32.1428)3 x 500 = 16604321.06 = 1660.43 ha - m
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A map has shrunk and the 15 cm reference line now measures 14 cm. If ...
To find the volume of the reservoir, we need to understand the relationship between the measurements on the map and the actual measurements in real life.
Given:
Original scale of the map: 1 cm = 30 m
Measured volume of the reservoir on the map: 500 m²
We are also given that the reference line on the map has shrunk from 15 cm to 14 cm.
Step 1: Find the scale conversion factor:
The original scale of the map is 1 cm = 30 m. This means that every 1 cm on the map represents 30 m in real life.
To find the scale conversion factor, we can set up a proportion:
(1 cm / 30 m) = (14 cm / x)
Cross-multiplying, we get:
x = (30 m * 14 cm) / 1 cm
x = 420 m
This tells us that 14 cm on the map represents 420 m in real life.
Step 2: Convert the measured area on the map to real-life area:
Since the area is measured in square meters, we need to square the scale conversion factor to convert the measured area on the map to real-life area.
Real-life area = (Measured area on the map) * (Scale conversion factor)^2
Real-life area = 500 m² * (420 m / 14 cm)^2
Real-life area = 500 m² * (420 m / 0.14 m)^2
Real-life area = 500 m² * (3000)^2
Real-life area = 500 m² * 9,000,000
Real-life area = 4,500,000,000 m²
Step 3: Convert the real-life area to hectares:
Since 1 hectare (ha) is equal to 10,000 square meters (m²), we can convert the real-life area to hectares.
Real-life area in hectares = Real-life area / 10,000
Real-life area in hectares = 4,500,000,000 m² / 10,000
Real-life area in hectares = 450,000 ha
Step 4: Convert the real-life area to volume:
Since the volume is measured in cubic meters (m³), we need to multiply the real-life area by the height or depth of the reservoir.
Assuming a depth of 1 meter, the volume of the reservoir in cubic meters is equal to the real-life area in hectares.
Volume of the reservoir = Real-life area in hectares
Volume of the reservoir = 450,000 ha
Step 5: Convert the volume to ha-m:
To convert the volume from cubic meters to hectare-meters (ha-m), we need to multiply the volume by 10,000.
Volume of the reservoir in ha-m = Volume of the reservoir * 10,000
Volume of the reservoir in ha-m = 450,000 ha * 10,000
Volume of the reservoir in ha-m = 4,500,000,000 ha-m
Rounded to 2 decimal places, the volume of the reservoir is between 1655 and 1665 ha-m.
Given:
Original scale of the map: 1 cm = 30 m
Measured volume of the reservoir on the map: 500 m²
We are also given that the reference line on the map has shrunk from 15 cm to 14 cm.
Step 1: Find the scale conversion factor:
The original scale of the map is 1 cm = 30 m. This means that every 1 cm on the map represents 30 m in real life.
To find the scale conversion factor, we can set up a proportion:
(1 cm / 30 m) = (14 cm / x)
Cross-multiplying, we get:
x = (30 m * 14 cm) / 1 cm
x = 420 m
This tells us that 14 cm on the map represents 420 m in real life.
Step 2: Convert the measured area on the map to real-life area:
Since the area is measured in square meters, we need to square the scale conversion factor to convert the measured area on the map to real-life area.
Real-life area = (Measured area on the map) * (Scale conversion factor)^2
Real-life area = 500 m² * (420 m / 14 cm)^2
Real-life area = 500 m² * (420 m / 0.14 m)^2
Real-life area = 500 m² * (3000)^2
Real-life area = 500 m² * 9,000,000
Real-life area = 4,500,000,000 m²
Step 3: Convert the real-life area to hectares:
Since 1 hectare (ha) is equal to 10,000 square meters (m²), we can convert the real-life area to hectares.
Real-life area in hectares = Real-life area / 10,000
Real-life area in hectares = 4,500,000,000 m² / 10,000
Real-life area in hectares = 450,000 ha
Step 4: Convert the real-life area to volume:
Since the volume is measured in cubic meters (m³), we need to multiply the real-life area by the height or depth of the reservoir.
Assuming a depth of 1 meter, the volume of the reservoir in cubic meters is equal to the real-life area in hectares.
Volume of the reservoir = Real-life area in hectares
Volume of the reservoir = 450,000 ha
Step 5: Convert the volume to ha-m:
To convert the volume from cubic meters to hectare-meters (ha-m), we need to multiply the volume by 10,000.
Volume of the reservoir in ha-m = Volume of the reservoir * 10,000
Volume of the reservoir in ha-m = 450,000 ha * 10,000
Volume of the reservoir in ha-m = 4,500,000,000 ha-m
Rounded to 2 decimal places, the volume of the reservoir is between 1655 and 1665 ha-m.
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A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer?
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A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer?.
A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A map has shrunk and the 15 cm reference line now measures 14 cm. If the original scale of the map is 1 cm = 30 m, find the volume of the reservoir(in ha-m, round up to 2 decimal places), if the measured volume of the reservoir on map is 500 m2.a)1655b)1665Correct answer is between '1655,1665'. Can you explain this answer?.
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