Question

if the area of the circular base of a cylinder is 22cm2 and its height is 10cm then the volume of the cylinder is. A). 2200cm2 b). 2200cm3 c). 220cm3 d). 220cm2​

Answer 1

Given:-

• Area of circular base of cylinder = 22cm²

• Height of cylinder = 10cm

To find:-

• Volume of cylinder

Solution:-

Area of circular base of cylinder = 22cm²

$:\implies$ πr² = 22cm²

$:\implies\sf \dfrac{22}{7} r^2 = 22$

$:\implies\sf r^2 = 22 \times \dfrac{7}{22}$

$:\implies$ r² = 7

$:\implies\sf \sqrt{r^2} = \sqrt{7}$

$:\implies\sf r = \sqrt{7} cm$

$\rule{200}3$

$:\implies\sf Volume_{(Cylinder)} = \pi r^2 h$

$:\implies\sf Volume_{(Cylinder)} = \dfrac{22}{7} \times \sqrt{7} \times \sqrt{7} \times 10$

$:\implies\sf Volume_{(Cylinder)} = \dfrac{22}{ \cancel{7}} \times \cancel{7} \times 10$

$:\implies\sf Volume_{(Cylinder)} = \bf{220cm^3}$

★ Therefore, Volume of Cylinder is = 220cm³

★ So, Option (C) is correct.

$\rule{200}3$

Answer 2

$\sf{\huge{\bold{\orange{\bigstar{\boxed{\boxed{Question}}}}}}}$

• If the area of the circular base of a cylinder is 22cm2 and its height is 10cm then the volume of the cylinder is.

$\sf{\huge{\bold{\orange{\bigstar{\boxed{\boxed{Solution}}}}}}}$

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

• $\sf Area = 22cm^2$
• $\sf height = 10 cm$

$\sf{\bold{\green{\underline{\underline{To\:find}}}}}$

• $\sf volume = ???$

$\sf{\bold{\red{\underline{\underline{Explanation }}}}}$

$\sf{\bold{\pink{\boxed{\boxed{ area = \pi r^2 }}}}}$

$\sf\implies {22 = \pi r^2 }$

$\sf\implies {22 = \dfrac{22}{7} r^2 }$

$\sf\implies{\cancel 22 \times \dfrac{7}{\cancel 22} = r^2 }$

$\sf\implies{ r = \sqrt {7}}$

$\sf{\bold{\pink{\boxed{\boxed{ radius = \sqrt {7} }}}}}$

$\sf{\bold{\pink{\boxed{\boxed{ volume = \pi r^2h }}}}}$

$\sf\implies volume = \dfrac{22}{7} {(\sqrt 7 )^2} \times 10$

$\sf\implies volume = \dfrac{22}{\cancel 7} \times {\cancel 7 } \times 10$

$\sf\implies volume = 22 \times 10$

$\sf \implies volume = 220cm^3$

$\sf{\bold{\pink{\boxed{\boxed{ volume \: = 220cm^3 \: = option \: C }}}}}$

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