Question
The Capacity of a closed cylindrical vessel of height 1m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Hint:
The capacity (or volume) of a closed cylindrical vessel with base radius r and height h, is
cubic units.
The correct answer is: 46.2 square metres of metal sheet would be needed to make it.
Explanations:
Step 1 of 2:
The capacity of a cylindrical vessel of height 1m is given by, 15.4 litres.
![therefore pi r squared h equals 15.4](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGoAAAARCAYAAAA1xDmVAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAhpJREFUeNpjYBi84D8U/wLio0CswjAKBjVgAuIsID43GhRDA/wYDYLBD+yB+OBoMAxuIAmto5RwyH+DFo/0AmpAXAvEFwjUrdgwscCHRPUDDkCBsgUaWdgAqIFxic5uWgzEaXgCktIA5gHia0MpokCRsw2I+fCoCQDi5QPYKqVFRM0E4mRyzCE122ZBiyN8RUA5VG09lJ0BxGegDQaYHCiSNAjYBdMvDMR9QPwSiN8Bcd4QjShrIN5LrjmkRtRCIJYF4jXQFA8Da6BlLzJYBcRPgbgHSx1ETBm/ChpZh4HYD1pXSUMjnIuMOoQUv1I7otigxbg8lXIm0eAuNMJg4D4Qi6OpuQXEQRTYcQtah/Ggib+D5rKBylGgTvonaKlQhMV92EAHEOdQsQglCrBAiz9k/hcsHdlvFHaEv2DJOSwUmktpRCG7wxjaQrxBoBjXg7ZsGegdUZZAvB+NvxdNjTmaGlKBORYzsdlN76IPG3Aj0A88yYA5REaXiIoE4vlI/HBo3YVPDaV2UMtcBhpEFKGRFbISDj7JAKgcoSbxNCBOROI3A/EUNDWToM1QcsEkNDuoZS4tIkoHWmdT1XxqRBTIUQZI/FYg3g3N3rA6ZR0Qe1EQULj0U2oupQG5Dlr8MkGxBzQ8gkhsTdO86ANFJvpItym0FbQYrWXGQYE9uPRTai6xCRlX0RQKbY3+gbplFdT/DIMtokYBDQAAUpq2yUm2fUEAAACidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDIyMzQ7PC9tbz48bWk+JiN4M0MwOzwvbWk+PG1zdXA+PG1pPnI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1pPmg8L21pPjxtbz49PC9tbz48bW4+MTUuNDwvbW4+PC9tYXRoPoQ22QQAAAAASUVORK5CYII=)
![not stretchy rightwards double arrow r squared equals 154 over 10 cross times 7 over 22 cross times 1 equals 49 over 10](data:image/png;base64,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)
.
Step 2 of 2:
The TSA (total surface area) of a closed cylindrical vessel is
sq. units, the term ‘’
indicates the surface area of the two closed bases.
![therefore pi r squared h plus 2 pi r squared](data:image/png;base64,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)
![equals 22 over 7 cross times 49 over 10 cross times 1 plus 2 cross times 22 over 7 cross times 49 over 10](data:image/png;base64,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)
![equals 1 over 10 left parenthesis 22 cross times 7 plus 44 cross times 7 right parenthesis](data:image/png;base64,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)
![equals 1 over 10 left parenthesis 154 plus 308 right parenthesis](data:image/png;base64,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)
![equals 462 over 10 equals 46.2 sq. straight m](data:image/png;base64,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)
Final Answer:
46.2 square metres of metal sheet would be needed to make it.
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Ram's mother is four times as old as Ram now. After sixteen years, she will be twice as old as Ram. Find their present ages.
Tanay obtained 98 marks in a mathematics test. His score is the highest in the class and it is also 8 more than three times the lowest score. Create the equation and calculate the lowest score.
Tanay obtained 98 marks in a mathematics test. His score is the highest in the class and it is also 8 more than three times the lowest score. Create the equation and calculate the lowest score.
Find three consecutive odd numbers whose sum is 159.
Find three consecutive odd numbers whose sum is 159.
Solve 3x - 2y = 6 and ![x over 3 minus y over 6 equals 1 half](data:image/png;base64,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)
Solve 3x - 2y = 6 and ![x over 3 minus y over 6 equals 1 half](data:image/png;base64,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)
Solve the following by substitution method 2x - 3y = 7 and x + 6y = 11.
Solve the following by substitution method 2x - 3y = 7 and x + 6y = 11.
Solve the following by using elimination method: 2x + y = 6 , 3y = 8 + 4x
Solve the following by using elimination method: 2x + y = 6 , 3y = 8 + 4x
Solve 2a – 3/b = 12 and 5a – 7/b = 1
Solve 2a – 3/b = 12 and 5a – 7/b = 1
Solve the following equations by using the elimination method: x - y = 1 , 3x - y = 9
Solve the following equations by using the elimination method: x - y = 1 , 3x - y = 9
Solve the following system of linear equations: 2x - 4y = 6 , x - 3y = 12
Solve the following system of linear equations: 2x - 4y = 6 , x - 3y = 12
Solve: x - 2y = 8 , 4x + 2y = 7 by using elimination method.
Solve: x - 2y = 8 , 4x + 2y = 7 by using elimination method.
![2 x minus y equals negative 4](data:image/png;base64,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)
![2 x plus y equals 4](data:image/png;base64,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)
For the solution of the system of equations above, what is the value of ?
Note:
The equations can be solved in many other ways like substitution
method which is: to eliminate one variable in any one of the
equations with the help of other equation. As we need to find the
value of x, we try to find the value of y in terms of x from one
equation. Then put that value of y in the other equation to get a linear equation in one variable , which is x.
![2 x minus y equals negative 4](data:image/png;base64,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)
![2 x plus y equals 4](data:image/png;base64,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)
For the solution of the system of equations above, what is the value of ?
Note:
The equations can be solved in many other ways like substitution
method which is: to eliminate one variable in any one of the
equations with the help of other equation. As we need to find the
value of x, we try to find the value of y in terms of x from one
equation. Then put that value of y in the other equation to get a linear equation in one variable , which is x.