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Question: ​A rectangular sheet of paper of length 35 cm and

Berikut ini adalah pertanyaan dari BloosmyFairy pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

Question: ​A rectangular sheet of paper of length 35 cm and breadth 28 cm is folded in two ways to form a cylinder. Find the difference in the volumes of cylinders formed.

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Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Given

  • A rectangular sheet of paper of length 35 cm and breadth 28 cm is folded in two ways to form a cylinder.

To find

  • The difference in the volumes of cylinders formed.

Solution

\begin{gathered}\\\bold\dag\:{\sf{\purple{Length\:of\: rectangular\:sheet}}} =\sf 35 cm \end{gathered}

\begin{gathered}\bold\dag\:{\sf{\purple{Breadth\:of\: rectangular\:sheet}}} =\sf 28 cm\\\\\end{gathered}

⠀⠀

A rectangular sheet is folded in two ways to form a cylinder

⠀⠀

\begin{gathered}\\\qquad\qquad\maltese\;\;\;\:{\underline{\sf{\green{First\:way :-}}}}\\\\\end{gathered}

⠀⠀

A rectangular sheet is folded along its breadth to form a cylinder

⠀⠀

\begin{gathered}\\\bold\dag\:{\sf{\blue{Breadth= height\:of\:a\:cylinder}}} =\sf 28 cm \end{gathered}

\begin{gathered}\bold\dag\:{\sf{\blue{Length = Circumference\:of\:a\: cylinder}}} =\sf 35 cm \\\\\end{gathered}

⠀⠀

Let's find out radius of a cylinder

⠀⠀

\begin{gathered}\\\bullet\:{\underline{\sf{\orange{Circumference\:of\:circle = 2\pi r = Length}}}}\\\\\end{gathered}

\begin{gathered}\implies\sf 35 = 2 \times \dfrac{22}{7} \times r \\\\\end{gathered}

\begin{gathered}\implies\sf 35 = \dfrac{44r}{7} \\\\\end{gathered}

\begin{gathered}\implies\sf 35 = \dfrac{44r}{7}\\\\\end{gathered}

\begin{gathered}\implies\sf r = \dfrac{35\times 7}{44}\\\\\end{gathered}

\begin{gathered}\implies\sf r = 5.5cm\\\end{gathered}

\begin{gathered}\therefore{\underline{\boxed{\sf{Radius\:of\:a\: cylinder = 5.5 cm}}}}\\\\\end{gathered}

\begin{gathered}\\\implies\sf \pi r^2 h \\\\\end{gathered}

\begin{gathered}\implies\sf \dfrac{22}{7}\times 5.5 \times 5.5 \times 28 \\\\\end{gathered}

\begin{gathered}\implies\sf 22\times 5.5 \times 5.5 \times 4 \\\\\end{gathered}

\begin{gathered}\implies\sf 2662cm^2\\\end{gathered}

\therefore{\underline{\boxed{\sf{Volume\:of\:a\: cylinder(V_1) = 2662 cm^3}}}}

⠀⠀

 ____________________________________________

⠀⠀\begin{gathered}\\\qquad\qquad\maltese\;\;\;\:{\underline{\sf{\green{Second\;way :-}}}}\\\\\end{gathered}

⠀⠀

A rectangular sheet is folded along its length to form a cylinder

⠀⠀

\begin{gathered}\\\bold\dag\:{\sf{\blue{Length= height\:of\:a\:cylinder}}} =\sf 35 cm \end{gathered}

\begin{gathered}\bold\dag\:{\sf{\blue{Breadth = Circumference\:of\:a\: cylinder}}} =\sf 28cm \\\\\end{gathered}

⠀⠀

Let's find out radius of a cylinder

⠀⠀

\begin{gathered}\\\bullet\:{\underline{\sf{\orange{Circumference\:of\:circle = 2\pi r = Breadth}}}}\\\\\end{gathered}

\begin{gathered}\implies\sf 28 = 2 \times \dfrac{22}{7} \times r \\\\\end{gathered}

\begin{gathered}\implies\sf \cancel\dfrac{28}{2} = \dfrac{22r}{7} \\\\\end{gathered}

\begin{gathered}\implies\sf 14 = \dfrac{22r}{7}\\\\\end{gathered}

\begin{gathered}\implies\sf r = \dfrac{14\times 7}{22}\\\\\end{gathered}

\begin{gathered}\implies\sf r = 4.4cm\\\end{gathered}

\begin{gathered}\therefore{\underline{\boxed{\sf{Radius\:of\:a\: cylinder = 4.4 cm}}}}\\\\\end{gathered}

\begin{gathered}\\ \\ \sf{\pink{Volume_ {( \: Cylinder)} = \pi r^2 h}} \\\\\end{gathered}

\begin{gathered}\implies\sf \dfrac{22}{7}\times 4.4 \times 4.4 \times 35 \\\\\end{gathered}

\begin{gathered}\implies\sf 22\times 4.4 \times 4.4 \times 5 \\\\\end{gathered}

\begin{gathered}\implies\sf 2129.6cm^2\\\end{gathered}

\begin{gathered}\therefore{\underline{\boxed{\sf{Volume\:of\:a\: cylinder(V_2) = 2129.6 cm^3}}}}\\\\\end{gathered}

⠀⠀

Difference between the volumes of cylinder formed

⠀⠀

\begin{gathered}\\\implies\sf V_1 - V_2 \\\\\end{gathered}

\begin{gathered}\implies\sf 2662 - 2129.6 \\\\\end{gathered}

\implies\sf 532.4 cm^3

\therefore{\underline{\boxed{\sf{Difference\:between\:in\:the\: volumes= 532.4 cm^3}}}} ___________________________________________

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Last Update: Sun, 06 Jun 21
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