Maths-
General
Easy
Question
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one fifth of litre?
Hint:
We find the capacity of the pen barrel, and then find the number of words accordingly.
The correct answer is: The required number of words is 45091.
Explanations:
Step 1 of 2:
Given, length of the barrel = height of barrel, h = 7cm
Base radius of the barrel, r = 5/2 mm = 2.5 mm = 0.25cm (since 1cm = 10mm)
Capacity of the barrel = volume of the barrel
![equals pi r squared h](data:image/png;base64,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)
![equals pi left parenthesis 0.25 right parenthesis squared cross times 7](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAARCAYAAAA42knSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAqtJREFUeNrtWU1kXFEUfkaMUVGyqiwqRFRUxRBZVERlE1lERIgaWXUTERHVTRfVVZXIKqJCVEVkESIqoqqMqjFGZBPVVYToejZZRMUYQ3IO33Bd595375t5ry8mH9/i3vfmvfPOd8/PvRME93DFDVgnVogDneyMJeJqSmxZhT0mZHD9tFPFGiIep8ymCuyyodapgrFz8trcQ+Im8QTcwpwJo8QD4hVS1m/ivCWtSVQxTCxb3veCWIox7brY+F+Qh2A6fhKnlfEU5kxg5xWI3Rg/xXMLgkNcUYZwOnrx7P4E/TRH/JwGwdaIy4JxG8K964IANvQR/7Qg2IpQV58Qv0G0pPAIiycXZwNxHRLab3HvD+KY9ntObRPCc8dxzQe1FgR7rkU1i/Q9JDU38Q70vSbhSCgZXnk07KN3iI/h3BlNiCntXq45WW3uUpgLMFf1dHilBcGysK8JFmvQ4/eSML5iLRLfJxXKFxCuib8IbxUN4XcNyzPrju/OoVkZFQSrQwgW4I1S98LeF6UJUAXyFasP39CVhFhdSIvq+J+jOI0WW+ke4qEhrar2DGP1nlkip94GX7BIRU+xmo3UeDtayxvHdPTLUg9sKbFqSIk5h5TYD7F8TiEmDC26nhKTFGwOGSAxcDe3rYxforbpKAppi2vdpMGxtqZjEK3vgwj21hyajqhi+abEDKI+n6RgvOl9pYw/ED85tvWzhj3HtqWt59q4HzHfP0O91bEM+9ohlk/TMRPTpjy04VBXyEdE04AWAaaNM6fT1xAgi48sGVJ3gL2RSwf3FZGTASdh66zHxjmqWK6i7WmLPXbwCtEPRkdQD3aF+/kccUhoHL4gVV3jaKrbIphrveXacI7G5hJROSLYFHY0FSeq+P7U4q4e/nY0FoP0/L3CdWshrY66BV6rymHvRQWmAAAAqnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz49PC9tbz48bWk+JiN4M0MwOzwvbWk+PG1vPig8L21vPjxtbj4wLjI1PC9tbj48bXN1cD48bW8+KTwvbW8+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4RDc7PC9tbz48bW4+NzwvbW4+PC9tYXRoPlQLCoQAAAAASUVORK5CYII=)
cm3
So, 310 words use up 1.375 cm3 of ink.
Step 2 of 2:
1/5th of litre = 1/51000cm3 = 200cm3
Now, 1.375cm3 of ink is used up by 310 words
200cm3 of ink will be used up by
= 45090.9
45091 words
Final Answer:
The required number of words is 45091.
Related Questions to study
Maths-
Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.Application
Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.Application
Maths-General
Maths-
Identify the parallel lines and perpendicular lines from the given set. Application
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2
Identify the parallel lines and perpendicular lines from the given set. Application
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2
Maths-General
Maths-
A line l touches the Y-axis at point 3 and has slope –3. Find the slope of the line perpendicular to the line l.
A line l touches the Y-axis at point 3 and has slope –3. Find the slope of the line perpendicular to the line l.
Maths-General
Maths-
Identify the equation of a line parallel to the line y = x – 1
Identify the equation of a line parallel to the line y = x – 1
Maths-General
Maths-
The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder?
The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder?
Maths-General
Maths-
Identify the equation of a line perpendicular to the line x/2 + y = -1
Identify the equation of a line perpendicular to the line x/2 + y = -1
Maths-General
Maths-
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis? Application
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis? Application
Maths-General
Maths-
Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.
Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.
Maths-General
Maths-
Find the equation of line such that its y-intercept is 20 and slope is ½.Application
Find the equation of line such that its y-intercept is 20 and slope is ½.Application
Maths-General
Maths-
Identify the line having y-intercept = 1/2
Identify the line having y-intercept = 1/2
Maths-General
Maths-
Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x. Application
Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x. Application
Maths-General
Maths-
Two solid cylinders with radii 5 cm and 10 cm and lengths of 7 cm and 5 cm respectively are melted and recast into a cylindrical disc of thickness 3 cm, Calculate its radius.
Two solid cylinders with radii 5 cm and 10 cm and lengths of 7 cm and 5 cm respectively are melted and recast into a cylindrical disc of thickness 3 cm, Calculate its radius.
Maths-General
Maths-
Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.Application
Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.Application
Maths-General
Maths-
A Cylinder tank has a 75 cm diameter and 1.8 m height. Find the capacity in litres to three significant figures?
A Cylinder tank has a 75 cm diameter and 1.8 m height. Find the capacity in litres to three significant figures?
Maths-General
Maths-
The graph shows the subscription cost to a certain club in town. Write an equation of the Application
line. Explain what the slope and y-intercept mean in this situation. Then find the total
cost for 2 years.
The graph shows the subscription cost to a certain club in town. Write an equation of the Application
line. Explain what the slope and y-intercept mean in this situation. Then find the total
cost for 2 years.
Maths-General