Question

The radius and height of a cylinder is in ratio 7:2. volume of cylinder is 8316 cm3 .find the radius and height of the cylinder .
help me it is urgent​

Answer 1

Given :

• The Radius and Height of a cylinder is in ratio 7:2.
• Volume of Cylinder is 8316 cm³ .

To Find :

• Radius and Height of the Cylinder .

Solution :

$\longmapsto\tt{Let\:Radius\:be=7x}$

$\longmapsto\tt{Let\:Height\:be=2x}$

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cylinder=\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{8316=\dfrac{22}{{\not{7}}}\times{{\not{7}}x}\times{7x}\times{2x}}$

$\longmapsto\tt{8316=22\times{{14x}^{3}}}$

$\longmapsto\tt{\cancel\dfrac{8316}{22}={14x}^{3}}$

$\longmapsto\tt{\cancel\dfrac{378}{14}={x}^{3}}$

$\longmapsto\tt{27={x}^{3}}$

$\longmapsto\tt\bf{3=x}$

Value of x is 3 .

Therefore :

$\longmapsto\tt{Radius\:of\:Cylinder=7(3)}$

$\longmapsto\tt\bf{21\:cm}$

$\longmapsto\tt{Height\:of\:Cylinder=2(3)}$

$\longmapsto\tt\bf{6\:cm}$

Answer 2

Answer:

Given :-

• The radius and height of a cylinder is in the ratio of 7 : 2.
• The volume of cylinder is 8316 cm³.

To Find :-

• What is radius and height of the cylinder.

Formula Used :-

$\clubsuit$ Volume of Cylinder Formula :

$\mapsto \sf\boxed{\bold{\pink{Volume_{(Cylinder)} =\: {\pi}r^2h}}}$

where,

• π = pie or 22/7
• r = Radius of Cylinder
• h = Height of Cylinder

Solution :-

Let,

$\mapsto \bf{Radius\: Of\: Cylinder =\: 7x\: cm}$

$\mapsto \bf{Height\: Of\: Cylinder =\: 2x\: cm}$

$\red{\bigstar}\: \: \sf\bold{\purple{According\: to\: the\: question\: :-}}$

$\implies \sf \dfrac{22}{7} \times (7x)^2 \times 2x =\: 8316$

$\implies \sf \dfrac{22}{7} \times 49x^2 \times 2x =\: 8316$

$\implies \sf \dfrac{22}{7} \times 98x^3 =\: 8316$

$\implies \sf x^3 =\: \dfrac{8316 \times 7}{22 \times 98}$

$\implies \sf x^3 =\: \dfrac{\cancel{58212}}{\cancel{2156}}$

$\implies \sf x^3 =\: 27$

$\implies \sf x =\: \sqrt[3]{27}$

$\implies \sf\bold{\green{x =\: 3}}$

Hence, the required radius and height of a cylinder are :

$\leadsto \sf\bold{Radius\: Of\: Cylinder\: :-}$

$\longrightarrow \sf 7x\: cm$

$\longrightarrow \sf 7(3)\: cm$

$\longrightarrow \sf\bold{\red{21\: cm}}$

$\leadsto \sf\bold{Height\: Of\: Cylinder\: :-}$

$\longrightarrow \sf 2x\: cm$

$\longrightarrow \sf 2(3)\: cm$

$\longrightarrow \sf\bold{\red{6\: cm}}$

$\therefore$ The radius and height of a cylinder is 21 cm and 6 cm respectively.