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Mensuration - Volume and Surface Areas

Multiple Choice Questions

111.

A conical flask is full of water. The flask has base radius r and height h. This water is poured into a cylindrical flask of base radius mr. The height of water in the cylindrical flask is

$straight h over 2 straight m squared$
$fraction numerator 2 straight h over denominator straight m end fraction$
$fraction numerator straight h over denominator 3 straight m squared end fraction$
$fraction numerator straight m over denominator 2 straight h end fraction$

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112.
The curved surface area and the total surface area of a cylinder are in the ratio 1 : 2. If the total surface area of the right cylinder is 616 cm², then its volume is

1632 cm³

1078 cm³

1232 cm³

1848 cm³

1078 cm³

Curved surface area of cylinder:
$equals space space space 2 πrh space cm squared$
Total surface area of cylinder:
$space equals space 2 πr left parenthesis straight h space plus space straight r right parenthesis space cm squared$
Now, according to the question,
$rightwards double arrow space space space space space fraction numerator 2 πrh over denominator 2 πr left parenthesis straight h plus space straight r right parenthesis end fraction space equals space 1 half rightwards double arrow space space space space fraction numerator straight h over denominator straight h plus straight r end fraction space equals space 1 half rightwards double arrow space space space 2 straight h space equals space straight h space plus space straight r rightwards double arrow space space space space straight h space equals space straight r$

Now, Total surface area = 616 cm^{2
$rightwards double arrow space space space space 2 πr left parenthesis straight h space plus space straight r right parenthesis space equals space 616 rightwards double arrow space space space space 2 πr left parenthesis straight r plus space straight r right parenthesis space equals space space 616 space space space space space space space space space space left parenthesis as space straight h space equals space straight r right parenthesis rightwards double arrow space space space space 2 πr left parenthesis 2 straight r right parenthesis space equals space 616 rightwards double arrow space space space space space space 4 πr squared space equals space space 616 therefore space space space space space space space space space space space space space space space space space straight r space equals space square root of fraction numerator 616 over denominator 4 straight pi end fraction end root space equals space square root of fraction numerator 616 space cross times space 7 over denominator 4 space cross times space 22 end fraction end root space equals space square root of 7 space cross times space 7 end root space equals space 7 space cm$}∴ Volume
$equals space πr squared straight h equals space 22 over 7 space cross times space open parentheses 7 space cross times 7 close parentheses space cross times space 7 space equals space 1078 space cm squared$