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Maths-

General

Easy

Question

From a solid wooden cylinder of 25 cm height and 6 cm diameter , two conical cavities are hollowed out , The diameters of the cones are also of 6 cm and the height is 10.5 cm, Find the volume of the remaining solid ?

hint Hint:

Volume of solid cylinder $equals 1 third pi r squared h$

The correct answer is: 508.93

Explanation:

We have given From a solid wooden cylinder of 25 cm height and 6 cm diameter , two conical cavities are hollowed out , The diameters of the cones are also of 6 cm and the height is 10.5 cm

We have to find the volume of the remaining solid.

Step 1 of 1:
Volume of the cylinder is
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell V equals pi r squared h end cell row cell equals pi left parenthesis 3 right parenthesis squared cross times 25 end cell row cell equals 225 pi end cell end table$
Volume of both cone will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell V equals 2 cross times 1 third pi r squared h end cell row cell equals 2 cross times 1 third pi left parenthesis 3 right parenthesis squared cross times 10.5 end cell row cell equals 63 pi end cell end table$
Volume of the remaining solid will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 225 pi minus 63 pi end cell row cell equals 162 pi end cell row cell equals 508.93 cm cubed end cell end table$

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