Question

a cylinder and a cone have equal bases. the height of the cylinder is 3 cm and the area of its base is 100 cm2 . the cone is placed volume of the solid figure so formed is 500 cm3 . find the total height of the figure.

Answer 1

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Answer 2

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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,

$= 3 + 6$

$= 9 cm$