Question

$\blue{Please}$$\pink{Answer }$$\blue{The}$$\pink{Question}$​

Answer 1

Given:

• The radius and height of a cylinder are in the ratio 2:3 .

• The volume of the cylinder is 16/7 cm³.

To find out:

Find the height of given cylinder?

Formula used:

Volume of cylinder = π × r² × h

Solution:

Let the radius of the base and height of the cylinder be 2x cm and 7x cm respectively.

According to the question,

Volume of cylinder = π × r² × h

★ Substituting the values in the above formula,we get:

⇒ 16/7 = 22/7 × ( 2x )² × 3x

⇒ 16/7 = 22/7 × 4x² × 3x

⇒ 4x² × 3x = 16/7 × 7/22

⇒ 12x³ = 16/22

⇒ 12x³ = 8/11

⇒ x³ = 8/11 × 12

⇒ x³ = 8/132

⇒ x³ = 0.06

⇒ x³ = 0.39

⇒ x = 0.39 ( approx )

Hence, Height of cylinder = 3x = 3 × 0.39 = 1.17 cm.

Answer 2

$\huge{\underline{\pink{\tt{Given,}}}}$

• The Radius and Height of a Cylinder are in the ratio 2:3.
• If the Volume of the Cylinder is 16/7 cm³.

$\huge{\underline{\pink{\tt{To \ Find,}}}}$

• The Height of Cylinder

$\huge{\underline{\pink{\tt{Formula \ Used :}}}}$

• $\underline{\boxed{\sf{Volume\:of\:Cylinder = \pi r^{2}h}}}$

$\huge{\underline{\pink{\tt{Solution :}}}}$

$\longrightarrow$ Suppose the Radius be 2a cm and the Height be 3a cm.

Now We Find Height with the Help of Volume :

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

$\implies \sf{\dfrac{16}{7} = \dfrac{22}{7} \times (2a)^{2} \times (3a)}$

$\implies \sf{\dfrac{16}{7} = \dfrac{22}{7} \times 4a^{2} \times 3a}$

$\implies \sf{\dfrac{16}{7} \times \dfrac{7}{22} = 12a^{3}}$

$\implies \sf{\dfrac{16}{22} = 12a^{3}$

$\implies \sf{a^{3} = \dfrac{16}{22} \times \dfrac{1}{12} }$

$\implies \sf{a^{3} = \dfrac{16}{264} }$

$\implies \sf{a^{3} = 0.06}$

$\implies \sf{a = \sqrt[3]{0.06}}$

$\implies \boxed{\sf{a = 0.391}}$ (Approx)

Therefore,

$\boxed{\red{\mathfrak{The\:Height\:of\:Cylinder = 3a = 3(0.391) = 1.73\:cm}}}$

$\rule{200}2$