Question

A cylindrr and a cone have equal baees. The height of the cylinder is 3 cm and the area of its base is 100 cm². The cone is placed upon the cylinder. Volume isbthe solid figure so formed is 500 cm³. Find the total height of the figure

Answer 1

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Lets find the radius of cylinder first,

Given the area of base if 100 sq. cm,

\pi r^2 = 100

r^2 = 100/ \pi

r = 10/ \sqrt{ \pi}

Now find the volume of cylinder,

= \pi r^2 h

= \pi * 100/ \pi * 3

'π' gets cancelled out,

= 300 cm^2

Now the height of cone,

1/3 \pi r^2 h = 500 - 300

1/3 * \pi * 100/ \pi * h = 200

'π' is cancelled again,

1/3 * 100h = 200

100h = 600

h = 600/100

h = 6 cm

Total height of the figure,

= 3 + 6

= 9 cm