Question

the radius and height of a cylinder are in the ratio 3:4 and it's volume is 38808cm find it's radius and height​

Answer 1

GIVEN :-

• the radius and height of a cylinder are in the ratio 3:4 .
• Volume of cylinder = 38808 cm³.

TO FIND :-

• The Radius and Height of the cylinder.

SOLUTION :-

Let the ratio constant be "x".

★ Radius = 3x.

★ Height = 4x.

$\\ : \implies \displaystyle \sf \:volume \: of \: cylinder = \pi r ^{2} h$

• h = Height of the cylinder.
• r = Radius of the cylinder.

$\\ \\ : \implies \displaystyle \sf \:38808 = \frac{22}{7} \times (3x) ^{2} \times 4x$

$: \implies \displaystyle \sf \:38808 = \frac{22}{7} \times 9x ^{2} \times 4x$

$: \implies \displaystyle \sf \:38808 = \frac{22}{7} \times 36x ^{3}$

$: \implies \displaystyle \sf \:36x ^{3} = \frac{38808 \times 7}{22}$

$: \implies \displaystyle \sf \:36x ^{3} = 1764 \times 7$

$: \implies \displaystyle \sf \:36x ^{3} = 12348$

$: \implies \displaystyle \sf \: x ^{3} = \frac{12348}{36}$

$: \implies \displaystyle \sf \: x ^{3} = 343$

$: \implies \displaystyle \sf \: x = \sqrt[3]{343}$

$: \implies \displaystyle \sf \: x = \sqrt[3]{7 ^{3} }$

$: \implies \underline{ \boxed{\displaystyle \sf \: x = 7}}$

Now by substituting the value of x we will find the radius and the height of the cylinder.

★ Radius = 3x = 3 × 7 = 21 cm

★ Height = 4x = 7 × 4 = 28 cm.

Answer 2

Answer:

✯ Given :-

• The radius and height of a cylinder are in the ratio of 3:4 and it's volume is 38808 cm.

✯ To Find :-

• What is the value of radius and height.

✯ Formula Used :-

$\boxed{\bold{\small{✮\: Volume\: of\: Cylinder\: =\: πr²h}}}$

✯ Solution :-

» Let, the radius be 3x and height be 4x.

➣ According to the question by using the formula we get,

⇒ 38808 = $\dfrac{22}{7}$ × (3x)² × 4x

⇒ 38808 = $\dfrac{22}{7}$ × 36x³

⇒ 36x³ = $\dfrac{38808 × 7}{22}$

⇒ 36x³ = $\dfrac{271656}{22}$

⇒ 36x³ = $\sf\dfrac{\cancel{271656}}{\cancel{22}}$

⇒ 36x³ = 12348

⇒ x³ = $\sf\dfrac{\cancel{12348}}{\cancel{36}}$

⇒ x³ = 343

⇒ x = $\sqrt[3]{343}$

⇒ x = $\sqrt[3]{(7)³}$

➥ x = 7

Hence,

❐ Radius of a cylinder = 3x = 3(7) = 21 cm

❐ Height of a cylinder = 4(x) = 4(7) = 28 cm

$\therefore$ The radius of a cylinder is 21 cm and the height of a cylinder is 28 cm.

________________________________