Question

The radius and height of a cylinder are in the ratio of 7:2 If the volume is 8316cm³, find radius and height

Answer 1

Answer:

Given :-

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

To Find :-

• What is the radius and height of a 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
• h = Height

Solution :-

Let,

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

$\longrightarrow \sf Height_{(Cylinder)} =\: 2x$

According to the question by using the formula we get,

$\implies \bf Volume_{(Cylinder)} =\: 8316$

$\implies \sf {\pi}r^2h =\: 8316$

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

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

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

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

$\implies \sf 2156x^3 =\: 58212$

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

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

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

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

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

★ Radius of Cylinder :-

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

$\leadsto \sf Radius_{(Cylinder)} =\: 7 \times 3$

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

★ Height of Cylinder :-

$\leadsto \sf Height_{(Cylinder)} =\: 2x$

$\leadsto \sf Height_{(Cylinder)} =\: 2 \times 3$

$\leadsto \sf\bold{\red{Height_{(Cylinder)} =\: 6\: cm}}$

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

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Answer 2

Answer:

Given :-

The radius and height of a cylinder are in the ratio of 7 : 2.

The volume of cylinder is 8316 cm³.

To Find :-

What is the radius and height of a cylinder.

Formula Used :-

\clubsuit♣ Volume Of Cylinder Formula :

\mapsto \sf\boxed{\bold{\pink{Volume_{(Cylinder)} =\: {\pi}r^2h}}}↦Volume(Cylinder)=πr2h

where,

π = Pie or 22/7

r = Radius

h = Height

Solution :-

Let,

\longrightarrow \sf Radius_{(Cylinder)} =\: 7x⟶Radius(Cylinder)=7x

\longrightarrow \sf Height_{(Cylinder)} =\: 2x⟶Height(Cylinder)=2x

According to the question by using the formula we get,

\implies \bf Volume_{(Cylinder)} =\: 8316⟹Volume(Cylinder)=8316

\implies \sf {\pi}r^2h =\: 8316⟹πr2h=8316

\implies \sf \dfrac{22}{7} \times (7x)^2 \times 2x =\: 8316⟹722×(7x)2×2x=8316

\implies \sf \dfrac{22}{7} \times (7x \times 7x) \times 2x =\: 8316⟹722×(7x×7x)×2x=8316

\implies \sf \dfrac{22}{7} \times 98x^3 =\: 8316⟹722×98x3=8316

\implies \sf 22 \times 98x^3 =\: 8316 \times 7⟹22×98x3=8316×7

\implies \sf 2156x^3 =\: 58212⟹2156x3=58212

\implies \sf x^3 =\: \dfrac{58212}{2156}⟹x3=215658212

\implies \sf x^3 =\: 27⟹x3=27

\implies \sf x =\: \sqrt[3]{27}⟹x=327

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

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

★ Radius of Cylinder :-

\leadsto \sf Radius_{(Cylinder)} =\: 7x⇝Radius(Cylinder)=7x

\leadsto \sf Radius_{(Cylinder)} =\: 7 \times 3⇝Radius(Cylinder)=7×3

\leadsto \sf\bold{\red{Radius_{(Cylinder)} =\: 21\: cm}}⇝Radius(Cylinder)=21cm

★ Height of Cylinder :-

\leadsto \sf Height_{(Cylinder)} =\: 2x⇝Height(Cylinder)=2x

\leadsto \sf Height_{(Cylinder)} =\: 2 \times 3⇝Height(Cylinder)=2×3

\leadsto \sf\bold{\red{Height_{(Cylinder)} =\: 6\: cm}}⇝Height(Cylinder)=6cm

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