Question

plzzz solve it.. ....​

Answer 1

Given :-

Common diameter of solid shapes is 4.2cm

Height of cylinderical portion(h)=12

Height of conical portion(H) is 7cm

To Find:-

We have to find the volume of toy

Solution :-

$\sf \Big[\purple{Volume\ of \ solid \ toy = V_{cylinder}+V_{cone}+V_{Hemisphere}}\Big]$

$\underline{\sf\ \ Volume s\ \ }\begin{cases}\sf{Cylinder= \pi r^2 h}\\\sf{Cone= \dfrac{1}{3}\pi r^2 h}\\\sf{Hemisphere= \dfrac{2}{3}\pi r^3}\end{cases}$

$:\implies\sf\ Volume_{toy}= \pi r^2 h+\dfrac{1}{3}\pi r^2 H+\dfrac{2}{3}\pi r^3\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2\Bigg\lgroup\ h+ \dfrac{1}{3}H+ \dfrac{2}{3}r\Bigg\rgroup\\ \\ \\ \therefore\sf\ H= 7cm\ ;\ \ h= 12cm\ \ ;\ \ r= 4.2/2=2.1cn\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2 \Bigg\lgroup\ 12+ \dfrac{1}{3}\times 7 + \dfrac{2}{3}\times 2.1\Bigg\rgroup\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2 \bigg\lgroup \ \dfrac{36+7+4.2}{3}\bigg\rgroup\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2 \bigg\lgroup \dfrac{47.2}{3}\bigg\rgroup\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \dfrac{22}{\cancel{7}}\times \cancel{2.1}\times \cancel{2.1}\times \dfrac{47.2}{\cancel{3}}\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= 22\times 0.3\times 0.7\times 47.2\\ \\ \\ \\ :\implies\underline{\boxed{\red{\sf\ Volume_{toy}= 218.064cm^3}}}$

Answer 2

Given :-

Common diameter of solid shapes is 4.2cm

Height of cylinderical portion(h)=12

Height of conical portion(H) is 7cm

To Find:-

We have to find the volume of toy

Solution :-

$\sf \Big[\purple{Volume\ of \ solid \ toy = V_{cylinder}+V_{cone}+V_{Hemisphere}}\Big]$

$\underline{\sf\ \ Volume s\ \ }\begin{cases}\sf{Cylinder= \pi r^2 h}\\\sf{Cone= \dfrac{1}{3}\pi r^2 h}\\\sf{Hemisphere= \dfrac{2}{3}\pi r^3}\end{cases}$

$:\implies\sf\ Volume_{toy}= \pi r^2 h+\dfrac{1}{3}\pi r^2 H+\dfrac{2}{3}\pi r^3\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2\Bigg\lgroup\ h+ \dfrac{1}{3}H+ \dfrac{2}{3}r\Bigg\rgroup\\ \\ \\ \therefore\sf\ H= 7cm\ ;\ \ h= 12cm\ \ ;\ \ r= 4.2/2=2.1cn\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2 \Bigg\lgroup\ 12+ \dfrac{1}{3}\times 7 + \dfrac{2}{3}\times 2.1\Bigg\rgroup\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2 \bigg\lgroup \ \dfrac{36+7+4.2}{3}\bigg\rgroup\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \pi r^2 \bigg\lgroup \dfrac{47.2}{3}\bigg\rgroup\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= \dfrac{22}{\cancel{7}}\times \cancel{2.1}\times \cancel{2.1}\times \dfrac{47.2}{\cancel{3}}\\ \\ \\ \\ :\implies\sf\ Volume_{toy}= 22\times 0.3\times 0.7\times 47.2\\ \\ \\ \\ :\implies\underline{\boxed{\red{\sf\ Volume_{toy}= 218.064cm^3}}}$