Question

What is the diameter of the cylinder

Answer 1

• Diameter of cylinder is 14 units.

Explamation :

Given :-

• Volume of cylinder = 245π cubic units
• Height of cylinder = 5 units

To Find :-

• Diameter of cylinder?

Solution :-

Firstly lets calculate radius of cylinder by using formula of volume of cylinder, as we know that;

• Volume of cylinder = πr²h

Putting all values we get;

➸ 245π = π × r² × 5

By cutting 'π' with 'π' we get;

➸ 245 = r² × 5

➸ 245/5 = r²

➸ 49 = r²

➸ √(49) = r²

➸ √(7 × 7) = r²

➸ 7 = r

➸ r = 7 units

• Hence, radius of cylinder is 7 units.

Now lets calculate its diameter, as we know that;

• Diameter = Radius × 2

Putting all values we get;

➸ Diameter = 7 × 2

➸ Diameter = 14 units

• Hence, diameter of cylinder is 14 units.

Answer 2

$\\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{blue}{Given \: :}}}}}}$

• Volume of Cylinder = 245 π cubic units.
• Height of Cylinder = 5 units.

$\\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{green}{To \: Find \: :}}}}}}$

• Diameter of Cylinder = ??

$\\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{aqua}{Solution \: :}}}}}}$

★ Calculating the Radius of the Cylinder;

$\begin{gathered} \\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{hotpink}{using \: formula \: :}}}}} } \\ \\ \end{gathered}$

$\red\bigstar { \underline{ \underline{\underline{\boxed{\color{brown}{\textbf{ \:Volume \: = \: πr²h }}}}}} }$

Where ,

• Volume = 245 π cubic units
• π = pi
• r = Radius
• h = height = 5 units

$\\ \sf \implies \: \:Volume \: = \: πr²h$

$\sf \implies \: \:275 \: \pi\: = \: π \: \times {r}^{2} \: \times \: 5$

$\sf \implies \: \:275 \: \cancel{ \pi}\: = \: \cancel{ \pi} \: \times {r}^{2} \: \times \: 5$

$\sf \implies \: {r}^{2}\: = \: \: \frac{275}{5}$

$\sf \implies \: {r}^{2}\: = \: \: \cancel\frac{275}{5}$

$\sf \implies \: {r}^{2}\: = \: \: 55$

$\sf \implies \: r\: = \: \: \sqrt{55 }$

$\bf \implies \: r\: = \: \: 5 \: units \:$

★ Calculating the Diameter of the Cylinder;

$\\ \sf \implies \: Diameter\: = \: \: Radius \: × \: 2$

$\\ \sf \implies \: Diameter\: = \: \: 5 \: × \: 2$

$\\ \sf \implies \: Diameter\: = \: \: 10 units ....$

henceforth, The Diameter of Cylinder is 10 units ..!!