Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.