Question

The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm square find the volume of the cylinder

Answer 1

h+r=35cm
surface area = 2πr(r+h)
3080=2×22/7×r×35
r = 14 cm
14+h=35
h= 21cm
volume = 22/7×14×14×21
= 66×196
=12936 cubic cm

Answer 2

Answer:

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Given :}}}}}}\end{gathered}$

• ➺ The sum of the height and the radius of a solid cylinder = 35 cm.
• ➺ Total surface area of cylinder = 3080 cm.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:To Find :}}}}}}\end{gathered}$

• ➺ Radius of cylinder
• ➺ Volume of the cylinder

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Using Formulae :}}}}}}\end{gathered}$

$\bigstar{\underline{\boxed{\bf{\red{TSA \: of \: cylinder = 2\pi r(r + h)}}}}}$

$\bigstar{\underline{\boxed{\bf{\red{Volume \: of \: cylinder = \pi {r}^{2}h}}}}}$

$\pink\bigstar$ Where

• ⟶ TSA = Total surface area
• ⟶ π = 22/7
• ⟶ r = radius
• ⟶ h = height

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Solution :}}}}}}\end{gathered}$

$\pink\bigstar$ Here

• ⟶ r + h = 35 cm
• ⟶ Total surface area of cylinder = 3080 cm.

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Firstly, Finding the radius of cylinder

${\dashrightarrow{\pmb{\sf{TSA \: of \: cylinder = 2\pi r(r + h)}}}}$

• Substuting the values

${\dashrightarrow{\sf{3080 = 2 \times \dfrac{22}{7} \times r(35)}}}$

${\dashrightarrow{\sf{3080 = 2 \times \dfrac{22}{7} \times r \times 35}}}$

${\dashrightarrow{\sf{3080 = 2 \times \dfrac{22}{\cancel{7}} \times r \times \cancel{35}}}}$

${\dashrightarrow{\sf{3080= 2 \times {22}\times r \times 5}}}$

${\dashrightarrow{\sf{3080= 220r}}}$

${\dashrightarrow{\sf{Radius = \dfrac{3080}{220}}}}$

${\dashrightarrow{\sf{Radius = \cancel{\dfrac{3080}{220}}}}}$

${\dashrightarrow{\sf{Radius = 14 \: cm}}}$

$\bigstar{\underline{\boxed{\bf{ \purple{Radius \: of \: cylinder = 14 \: cm}}}}}$

∴ The radius of Cylinder is 14 cm.

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Now, Finding the height of cylinder

$\dashrightarrow{\pmb{\sf{Radius + Height = 35 \: cm}}}$

• Substuting the values

$\dashrightarrow{\sf{14+ Height = 35 \: cm}}$

$\dashrightarrow{\sf{Height = 35 - 14}}$

$\dashrightarrow{\sf{Height = 21 \: cm}}$

$\bigstar{\underline{\boxed{\bf{\purple{Height = 21 \: cm}}}}}$

∴ The height of cylinder is 21 cm.

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Now, Finding the volume of cylinder

${\dashrightarrow{\pmb{\sf{Volume \: of \: cylinder = \pi {r}^{2}h}}}}$

• Substuting the values

${\dashrightarrow{\sf{Volume \: of \: cylinder = \dfrac{22}{7} \times {(7)}^{2}\times 21}}}$

${\dashrightarrow{\sf{Volume \: of \: cylinder = \dfrac{22}{7} \times {(7 \times 7)}\times 21}}}$

${\dashrightarrow{\sf{Volume \: of \: cylinder = \dfrac{22}{\cancel{7}} \times {(14 \times 14)}\times \cancel{21}}}}$

${\dashrightarrow{\sf{Volume \: of \: cylinder = 22\times156 \times 3}}}$

${\dashrightarrow{\sf{Volume \: of \: cylinder = 12,936 \: {cm}^{2} }}}$

$\bigstar{\underline{\boxed{\bf{\purple{Volume \: of \: cylinder = 12,936 \: {cm}^{2}}}}}}$

∴ The volume of cylinder is 12,936 cm².

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Diagram :}}}}}}\end{gathered}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{14\ cm}}\put(9,17.5){\sf{21\ cm}}\end{picture}$

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Learn More :}}}}}}\end{gathered}$

⟶ Volume of cylinder = πr²h

⟶ T.S.A of cylinder = 2πrh + 2πr²

⟶ Volume of cone = ⅓ πr²h

⟶ C.S.A of cone = πrl

⟶ T.S.A of cone = πrl + πr²

⟶ Volume of cuboid = l × b × h

⟶ C.S.A of cuboid = 2(l + b)h

⟶ T.S.A of cuboid = 2(lb + bh + lh)

⟶ C.S.A of cube = 4a²

⟶ T.S.A of cube = 6a²

⟶ Volume of cube = a³

⟶ Volume of sphere = 4/3πr³

⟶ Surface area of sphere = 4πr²

⟶ Volume of hemisphere = ⅔ πr³

⟶ C.S.A of hemisphere = 2πr²

⟶ T.S.A of hemisphere = 3πr²

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\textsf{\textbf{\:Request :}}}}}}\end{gathered}$

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