Question

a solid is in a shape of cone on a hemisphere the ratio of each of them being 3.5 cm and then the total height of a solid is 9.5 cm find the volume of the solid

Answer 1

Calculate last expressions..

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Height of the solid

= 9.5 cm

$\Large{\boxed{\sf\:{Radius\;of\;the\;cone = Radius\;of\; the\;hemisphere }}}$

Hence,

r = 3.5 cm

Also,

$\Large{\boxed{\sf\:{Radius\;of\;the\;hemisphere = Height\;of\; the\;hemisphere }}}$

= 3.5 cm

Now we have to calculate

Height of cone,

$\Large{\boxed{\sf\:{Height\;of\;the\;solid - Height\;of\; the\;hemisphere }}}$

Hence,

h = 9.5 - 3.5

h = 6

Hence,

Height of cone = 6 cm

Also we know that,

Volume of solid

$\Large{\boxed{\sf\:{Volume\;of\;the\;cone + Volume\;of\; the\;hemisphere }}}$

Using formula

${\boxed{\sf\:{\dfrac{1}{3}\pi r^2h+\dfrac{2}{3}\pi r^3}}}$

$\tt{\rightarrow\dfrac{1}{3}\pi r^2(h+2r)}$

$\tt{\rightarrow\dfrac{1}{3}\times\dfrac{22}{7}\times 3.5\times 3.5\times(6+2\times 3.5)}$

$\tt{\rightarrow\dfrac{1}{3}\times\dfrac{22}{7}\times 3.5\times 3.5\times(6+7)}$

$\tt{\rightarrow\dfrac{1}{3}\times\dfrac{22}{7}\times 3.5\times 3.5\times(13)}$

$\tt{\rightarrow\dfrac{1}{3}\times 22\times 0.5\times 3.5\times(13)}$

$\tt{\rightarrow\dfrac{500.5}{3}}$

= 166.83 cm³

Therefore we get,

Volume of the solid = 166.83 cm³