Question

The volume of a right circular cylinder of height 7 cm is equal to that of a cube of edge 22 cm. Find
(a) the diameter of the base and (b) the curved surface area of the cylinder,​

Answer 1

${\boxed{\mathtt{\purple{Given}}}}$

• Volume of Cylinder = Volume of Cube
• Height of cylinder = 7 cm
• Edge of cube = 22 cm

${\boxed{\mathtt{\purple{To\: find}}}}$

• Base area of cylinder .
• CSA of cylinder .

${\boxed{\mathtt{\purple{Solution}}}}$

${\mathtt{Formulae}}$

${\mathtt{Volume \: of \: Cube \:=\: {a}^{3}\:here\:a\:=\:Side}}$

${\mathtt{Volume\:of\: Cylinder\:=\:\pi\:{r}^{2}\:h}}$

${\mathtt{Curved\: Surface\:area\:=\:2\:\pi\:r\:h}}$

${\mathtt{Base \:area \:=\: \pi\: {r}^{2} }}$

⇝ Volume of cylinder = Volume of cube.

Volume of cylinder :-

⇝ π × r² × 7

$⇝ \: \frac{22}{7} \: \times \: {r}^{2} \: \times 7$

⇝ 22r² = Volume of cylinder .

Volume of cube :-

⇝ a³

⇝( 22)³

⇝ 10648 cm³ = Volume of cube .

⇝ 22r² = 10648

$⇝ \: {r}^{2} \: = \: \frac{10648}{22} \: = \: 484$

⇝ r² = 484

⇝ r² = 22²

⇝ radius = 22cm

Diameter = 2 × radius

${\boxed{\boxed{\mathtt{Diameter\:=\:44\:cm }}}}$

Curved surface area :-

⇝ 2πrh

⇝ 2 × 22 × 7 × $\frac{22}{7}$

⇝ 2 × 22 × 22

⇝ 484 × 2 = 968 cm ²

${\boxed{\boxed{\mathtt{Curved\: Surface\:Area\:=\: 968 \:{cm}^{2}}}}}$

Answer 2

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer:-}}}}}}$

Given :-

Volume of Cylinder = Volume of Cube

Height of cylinder = 7 cm

Edge of cube = 22 cm

To Find :-

Base area of cylinder

CSA of cylinder

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Solution:-}}}}}}$

${\mathtt{Volume \: of \: Cube \:=\: {a}^{3}\:here\:a\:=\:Side}}$

Volume of Cylinder= πr ²h

${\mathtt{Curved\: Surface\:area\:=\:2\:\pi\:r\:h}}$

Base area =πr ²

⇝ Volume of cylinder = Volume of cube.

Volume of cylinder :-

=> π × r² × 7

=>22r² = Volume of cylinder .

Volume of cube :-

=> a³

=>( 22)³

=> 10648 cm³ = Volume of cube .

=> 22r² = 10648

$\begin{lgathered}⇝ \: {r}^{2} \: = \: \frac{10648}{22} \: = \: 484 \\\end{lgathered}$

=> r² = 484

=> r² = 22²

=> radius = 22cm

=> Diameter = 2 × radius

=> Diameter=44cm

Curved surface area :-

=> 2πrh

=> 2 × 22 × 7 × 22/7

=> 2 × 22 × 22

=> 484 × 2 = 968 cm ²

${\red{\boxed{\boxed{\mathtt{Curved\: Surface\:Area\:=\: 968 \:{cm}^{2}}}}}}$