[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 ..!!
