Question

The radius and height of a cylinder is in ratio 7:3. volume of cylinder is 12475 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 7:3.
• Volume of Cylinder is 12475 cm³ .

To Find :

• Radius and Height of the Cylinder .

Solution :

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

$\longmapsto\tt{Let\:Height\:be=3x}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{12475=\dfrac{22}{{\not{7}}}\times{{\not{7}}x}\times{7x}\times{3x}}$

$\longmapsto\tt{12475=22\times{{21}^{3}}}$

$\longmapsto\tt{\cancel\dfrac{12475}{22}={21x}^{3}}$

$\longmapsto\tt{\cancel\dfrac{567}{21}={x}^{3}}$

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

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

Value of x is 3 .

Therefore :

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

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

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

$\longmapsto\tt\bf{9\:cm}$

Answer 2

Answer:

Given :-

• The radius and height of a cylinder is in the ratio of 7 : 3.
• The volume of cylinder is 12475 cm³.

To Find :-

• What is the 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 or 3.14
• r = Radius of Cylinder
• h = Height of Cylinder

Solution :-

Let,

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

$\mapsto \bf{Height\: Of\: Cylinder =\: 3x\: cm}$

$\purple{\bigstar}\: \: \bf{According\: to\: the\: question\: by\: using\: the\: formula\: we\: get\: :-}$

$\implies \sf \dfrac{22}{7} \times (7x) \times 3x =\: 12475$

$\implies \sf \dfrac{22}{7} \times 49x^2 \times 3x =\: 12475$

$\implies \sf \dfrac{22}{\cancel{7}} \times {\cancel{147}}x^3 =\: 12475$

$\implies \sf 22 \times 21x^3 =\: 12475$

$\implies \sf x =\: \dfrac{12475}{22 \times 21}$

$\implies \sf x^3 =\: \dfrac{\cancel{12475}}{\cancel{462}}$

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

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

$\implies \sf\bold{\purple{x =\: 3\: cm}}$

Hence, the required radius and height of cylinder are :

❒ Radius of Cylinder :

$\longrightarrow \sf Radius_{(Cylinder)} =\: 7x\: cm$

$\longrightarrow \sf Radius_{(Cylinder)} =\: 7(3)\: cm$

$\longrightarrow \sf\bold{\red{Radius_{(Cylinder)} =\: 21\: cm}}$

❒ Height of Cylinder :

$\longrightarrow \sf Height_{(Cylinder)} =\: 3x\: cm$

$\longrightarrow \sf Height_{(Cylinder)} =\: 3(3)\: cm$

$\longrightarrow \sf\bold{\red{Height_{(Cylinder)} =\: 9\: cm}}$

$\therefore$ The radius and height of a cylinder is 21 cm and 9 cm respectively.