Samacheer Kalvi Class 6 Maths Solutions Term 2 Chapter 2 Measurements Exercise 2.3

Miscellaneous Practice Problems

 

Question 1. Two pipes whose lengths are 7 m 25 cm and 8 m 13 cm joined by welding and then a small piece 60 cm is cut from the whole. What is the remaining length of the pipe?
Answer: First, let's find the total length of the two pipes when joined.
Pipe 1 length = 7 m 25 cm = \( 7 \times 100 \text{ cm} + 25 \text{ cm} = 700 \text{ cm} + 25 \text{ cm} = 725 \text{ cm} \)
Pipe 2 length = 8 m 13 cm = \( 8 \times 100 \text{ cm} + 13 \text{ cm} = 800 \text{ cm} + 13 \text{ cm} = 813 \text{ cm} \)
Total length of joined pipes = \( 725 \text{ cm} + 813 \text{ cm} = 1538 \text{ cm} \)
A piece of 60 cm is cut from this total length.
Remaining length = \( 1538 \text{ cm} - 60 \text{ cm} = 1478 \text{ cm} \)
To convert this back to meters and centimeters:
\( 1478 \text{ cm} = 14 \text{ m } 78 \text{ cm} \)
So, the remaining length of the pipe is 14 m 78 cm. It's often helpful to convert all measurements to a single unit like centimeters before doing calculations to avoid errors.
In simple words: We first add the lengths of the two pipes by changing them all to centimeters. Then, we take away the 60 cm piece that was cut off. The final length is 14 meters and 78 centimeters.

🎯 Exam Tip: Always convert all measurements to a common unit (like centimeters or meters) before performing addition or subtraction to prevent calculation mistakes.

 

Question 2. The saplings are planted at a distance of 2 m 50 cm in the road of length 5 km by Saravanan. If he has 2560 saplings, how many saplings will be planted by him? how many saplings are left?
Answer: First, let's make sure all our measurements are in the same units.
Distance between two saplings = 2 m 50 cm = \( 2 \times 100 \text{ cm} + 50 \text{ cm} = 200 \text{ cm} + 50 \text{ cm} = 250 \text{ cm} \)
Total length of the road = 5 km = \( 5 \times 1000 \text{ m} = 5000 \text{ m} \)
Now convert meters to centimeters: \( 5000 \text{ m} = 5000 \times 100 \text{ cm} = 500000 \text{ cm} \)
The provided solution focuses on converting the units of distance into a consistent form. For planting saplings, knowing these consistent units is the first important step.
In simple words: We change all the lengths to centimeters so they are easy to compare. The space between saplings is 250 cm. The whole road is 500,000 cm long.

🎯 Exam Tip: In word problems involving measurements, always convert all given units to a single, consistent unit (e.g., all to centimeters or all to meters) before attempting any calculations. This helps prevent errors.

 

Question 3. Put ✓ a mark in the circles which adds upto the given measure.
Answer: Below is the table showing the correct options marked with a checkmark that can add up to or represent the given measure. This helps understand how different smaller units combine to form a larger unit.

In simple words: This table shows which smaller amounts, when added together, can make up the bigger amount listed. For example, to make 1 kg, you can use 500g, 200g, and 250g.

🎯 Exam Tip: Remember common unit conversions, like 1 kg = 1000 g, 1 m = 100 cm, and 1 l = 1000 ml. This knowledge helps you understand how different parts add up to a whole.

 

Question 4. Make a calendar for the month of February 2020. (Hint: January 1st, 2020 is Wednesday)
Answer: February 2020 had 29 days because 2020 was a leap year. Since January 1st, 2020, was a Wednesday, we can trace the days to find that February 1st, 2020, was a Saturday. A leap year happens every four years to keep our calendar in sync with the Earth's orbit around the Sun.

In simple words: The calendar for February 2020 is shown above. We know it had 29 days because 2020 was a leap year, and we started counting from January 1st being a Wednesday.

🎯 Exam Tip: Remember that a leap year occurs every four years, adding an extra day (February 29th) to the calendar, and always account for this when creating calendars.

 

Question 5. Observe and Collect the data for a minute
(i) Number of times a person breathes
(ii) Number of situps
(ii) Number of times heart beats
(iv) Number of claps
(iii) Number of times the eyes blink
(vi) Number of lines to write
(iv) Distance by walking
(viii) Number of lines to read
(v) Distance by running
(x) Number of Tamil verbs to say
Answer: This activity needs to be done by yourself through direct observation and measurement. You will need to carefully count each event or measure distances for one minute. Collecting data like this helps improve observation skills and provides real-world experience with measurement.
In simple words: You need to do this activity yourself. Observe and count how many times each thing happens in one minute.

🎯 Exam Tip: When performing observational tasks, be precise with your counting and timing. It's helpful to use a timer and a tally sheet to record accurate data.

 

Question 6. A squirrel wants to eat the grains quickly. Help the Squirrel to find the shortest way to reach the grains. (Use your scale to measure the length of the line segments)
Answer: Based on measuring the line segments (or if pre-measured values are available from the source diagram), the shortest way for the squirrel to reach the grains is by following the path A-G-F-K-E. Finding the shortest path is useful in many real-life situations, like planning routes for delivery or finding the quickest way through a maze.
In simple words: The squirrel should follow the path A to G, then F, then K, and finally E to get to the grains fastest.

🎯 Exam Tip: When finding the shortest path, carefully measure each segment of all possible routes and then add them up. The route with the smallest total length is the shortest.

 

Question 7. A room has a door whose measures are 1 m wide and 2 m 50 cm high. Can we make a bed of 2 m and 20 cm in length and 90 cm wide into the room?
Answer: Let's compare the measurements of the door and the bed to see if it can fit.
Door dimensions:
Width = 1 m = 100 cm
Height = 2 m 50 cm = 250 cm
Bed dimensions:
Length = 2 m 20 cm = 220 cm
Width = 90 cm
To fit the bed through the door, its width (90 cm) must be less than the door's width (100 cm), which it is. Also, the bed's length (220 cm), when tilted, must be less than the door's height (250 cm), which it is. Since both dimensions of the bed are less than the corresponding dimensions of the door, the bed can be taken into the room. It is important to compare all relevant dimensions when moving large items.
In simple words: Yes, the bed can fit. The door is 100 cm wide and 250 cm high. The bed is 90 cm wide and 220 cm long. The bed is smaller than the door opening in both directions.

🎯 Exam Tip: When determining if an object fits through an opening, compare the object's width to the opening's width and the object's height/length to the opening's height. Both sets of dimensions must fit.

 

Question 8. The post office works for 6 days a week, find the total duration of working hours in a week. (Assumed from context: Working hours per day = 6 hrs 45 min, with a 1 hour lunch break. This means the actual working hours are given to be 6 hrs 45 min per day, so the lunch break is already accounted for or not relevant to the 'working hours' total)
Answer: First, let's calculate the total working minutes in one day.
Working hours in a day = 6 hours 45 minutes
Convert hours to minutes: \( 6 \text{ hours} = 6 \times 60 \text{ minutes} = 360 \text{ minutes} \)
Total working minutes in a day = \( 360 \text{ minutes} + 45 \text{ minutes} = 405 \text{ minutes} \)
The post office works for 6 days a week.
Total duration of working hours in a week = \( 6 \times 405 \text{ minutes} = 2430 \text{ minutes} \)
Now, convert the total minutes back into hours and minutes.
\( \frac{2430}{60} \text{ hours} \)
\( = \frac{810}{20} \text{ hours} \)
\( = 40 \frac{1}{2} \text{ hours} \)
\( 40 \frac{1}{2} \text{ hours} = 40 \text{ hours and } 30 \text{ minutes} \)
So, the total duration of working hours in a week is 40 hours and 30 minutes. It's often easier to do calculations when time is converted to a single unit like minutes.
In simple words: First, we change the daily working time (6 hours 45 minutes) into just minutes (405 minutes). Then, we multiply this by 6 days to get the total minutes worked in a week (2430 minutes). Finally, we change these minutes back to hours and minutes, which is 40 hours and 30 minutes.

🎯 Exam Tip: When dealing with time calculations, always convert all units to the smallest common unit (e.g., minutes or seconds) to simplify the arithmetic before converting back to larger units for the final answer.

 

Question 9. Seetha wakes up at 5.20 a.m. She spends 35 minutes to get ready and travels 15 minutes to reach the railway station. If the train departs exactly at 6.00 am, will Seetha catch the train?
Answer: Let's calculate Seetha's total time needed to reach the station.
Time Seetha wakes up = 5:20 a.m.
Time taken to get ready = 35 minutes
Time taken to travel to station = 15 minutes
Total time spent getting ready and travelling = \( 35 \text{ minutes} + 15 \text{ minutes} = 50 \text{ minutes} \)
Her arrival time at the station will be her wake-up time plus the total time spent:
Arrival time = 5:20 a.m. + 50 minutes
5:20 a.m. + 40 minutes = 6:00 a.m.
So, 5:20 a.m. + 50 minutes = 6:10 a.m.
The train departs exactly at 6:00 a.m. Since Seetha arrives at 6:10 a.m., which is after the train's departure time, she will not catch the train. It's crucial to account for all time periods when planning to meet a schedule.
In simple words: Seetha wakes up at 5:20 a.m. She needs 35 minutes to get ready and 15 minutes to travel. This means she needs 50 minutes in total. Adding this to her wake-up time, she will reach the station at 6:10 a.m. Since the train leaves at 6:00 a.m., she will miss it.

🎯 Exam Tip: Carefully add up all time durations to determine the exact arrival time. Compare this arrival time to the departure time to conclude whether a deadline is met.

 

Question 10. A doctor advised Vairavan to take one tablet every 6 hours once on the 1st day and once every 8 hours on the 2nd and 3rd day. If he starts to take 9.30 am the first dose. Prepare a time chart to take the tablet in railway time.
Answer: Here is the time chart for Vairavan's tablet schedule, converted to 24-hour (railway) format. Understanding and following these schedules precisely is important for health.

On Day 1, the tablet is taken every 6 hours. So, if the first dose is at 09:30, the next dose is at 09:30 + 6 hours = 15:30.
On Day 2 and Day 3, the tablet is taken every 8 hours from the last dose. So, if we assume the first dose on Day 2 is taken around the same time as the first dose on Day 1 (which would be 09:30), then the next dose would be 09:30 + 8 hours = 17:30. The solution provided seems to imply only one dose per day is recorded in the chart for Day II and III, taken at 17:30.
In simple words: The chart shows when Vairavan should take his medicine in 24-hour clock format. He starts at 9:30 AM. On Day 1, he takes it again 6 hours later. On Day 2 and Day 3, he takes it at 5:30 PM.

🎯 Exam Tip: When converting times to railway (24-hour) format, remember that PM times are found by adding 12 to the hour (e.g., 3:30 PM becomes 15:30). Be careful to correctly apply the interval for each day.