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what is the diameter of the cylinder

What Is The Diameter Of The Cylinder class=

Sagot :

TwinklingStar

[tex] \\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{blue}{Given \: :}}}}}} \\ \\ [/tex]

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

[tex] \\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{green}{To \: Find \: :}}}}}} \\ \\ [/tex]

  • Diameter of Cylinder = ??

[tex]\\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{aqua}{Solution \: :}}}}}}\\ \\ [/tex]

★ Calculating the Radius of the Cylinder;

[tex]\begin{gathered} \\ \maltese \: \: \: \: \large{\underline{\underline{\pmb{\textsf{\color{hotpink}{using \: formula \: :}}}}} } \\ \\ \end{gathered} [/tex]

[tex]\red\bigstar { \underline{ \underline{\underline{\boxed{\color{brown}{\textbf{ \:Volume \: = \: πr²h }}}}}} }\\ \\ [/tex]

Where ,

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

[tex] \\ \sf \implies \: \:Volume \: = \: πr²h \\\\ [/tex]

[tex] \sf \implies \: \:275 \: \pi\: = \: π \: \times {r}^{2} \: \times \: 5 \\ \\ [/tex]

[tex] \sf \implies \: \:275 \: \cancel{ \pi}\: = \: \cancel{ \pi} \: \times {r}^{2} \: \times \: 5\\ \\ [/tex]

[tex] \sf \implies \: {r}^{2}\: = \: \: \frac{275}{5} \\ \\ [/tex]

[tex] \sf \implies \: {r}^{2}\: = \: \: \cancel\frac{275}{5} \\ \\ [/tex]

[tex] \sf \implies \: {r}^{2}\: = \: \: 55 \\ \\ [/tex]

[tex] \sf \implies \: r\: = \: \: \sqrt{55 }\\ \\ [/tex]

[tex] \bf \implies \: r\: = \: \: 5 \: units \: \\ \\ [/tex]

★ Calculating the Diameter of the Cylinder;

[tex]\\ \sf \implies \: Diameter\: = \: \: Radius \: × \: 2 \\ \\ [/tex]

[tex]\\ \sf \implies \: Diameter\: = \: \: 5 \: × \: 2 \\ \\ [/tex]

[tex]\\ \sf \implies \: Diameter\: = \: \: 10 units .... \\ \\ [/tex]

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

007Boy
  • 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.

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