Question

The volume of a cylindrical bucket is 660cm3 and its height is 11cm.

Find out the area of the base of the bucket. 

​

Answer 1

⇝ Given :-

• The volume of a cylindrical bucket is 660 cm³.

• Height of Bucket = 11 cm.

⇝ To Find :-

Area of Base of Bucket.

⇝ Solution :-

We Know Volume of Cylinder is :

$\large{\orange{ \underbrace{ \underline{\bf\pmb{V_{Cylinder} = \pi r^2h}}}}}$

Where,

• r = Base Radius of Cylinder.

• h = Height of Cylinder.

We Have :-

• Height of Bucket = h = 11 cm.

• Volume of Bucket = V = 660 cm³

Let Base Radius of Bucket be = r.

Hence,

★ Using Formula of Volume :

$:\longmapsto\pi {\text r}^{2} \times 11 = 660$

$:\longmapsto\pi {\text r}^{2} = \cancel\frac{660}{11}$

$\purple{ \Large :\longmapsto \underline {\boxed{{\pmb{\pi {r}^{2} = 60 \: {cm}^{2} }} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Area \: of \: Base =60 \: {cm}^{2} }}}}}$

Answer 2

$\frak{Given}\:\begin{cases}\:\quad\sf The \: Volume \:of \: a \:Cylindrical\:Bucket\:is \:\pmb{\frak{ 660\:cm^3\:}}\:\\\sf \:\quad The \:Height \:of \:Bucket\:is \:\pmb{\frak{ 11 \:cm \:}}\:\end{cases}$

Need To Find : The Area of the Base of the Cylindrical Bucket ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀▪︎We've Provided with the Volume and Height of Cylindrical Bucket and We have to find Area of the Base of the Cylindrical Bucket .

》 The Formula for Volume of Cylinder is Given by —:

$\qquad \star\:\pmb{\underline {\boxed {\frak{ \:Volume \:_{\:(Cylinder)}\:=\: \bigg\lgroup \:\pi\:r^2\:h\:\bigg\rgroup\:\:cu.units \:}}}}\:$

Where ,

• Volume of Cylinder is 660 cm³ &
• Height [ h ] of Cylinder is 11 cm .

$\qquad \dag\:\underline {\frak{ \:Substituting \:Known \:Values \:in \:Given \:Formulae \:\::\:}}$

$\qquad \twoheadrightarrow \:\sf \:Volume \:_{\:(Cylinder)}\:=\: \bigg\lgroup \:\pi\:r^2\:h\:\bigg\rgroup \\\\\\ \qquad \twoheadrightarrow \:\sf \:660\:=\: \bigg\lgroup \:\pi\:r^2\:(11)\:\bigg\rgroup \\\\\\ \qquad \twoheadrightarrow \:\sf \:\pi\:r^2\:=\:\dfrac{660}{11}\: \\\\\\ \qquad \twoheadrightarrow \:\sf \:\pi\:r^2\:=\:60\: \\\\\\ \qquad \twoheadrightarrow \:\sf \:Area_{\:(\:Base\:)}\:=\:60\: \qquad \qquad \because \bigg\lgroup \:Area_{\:(Base)\:}\:=\:\pi \:r^2\:\bigg\rgroup \\\\\\ \qquad \twoheadrightarrow \underline {\pmb{\boxed {\frak{\purple { \: \:Area_{\:(\:Base\:)}\:=\:60\:cm^2\:}}}}}\:\:\bigstar \:$

∴ Hence , Area of  Base of Cylinder Bucket is 60 cm² .