[tex] \tt \: The \: area \: of \: the \: circle \: is \: 154 sq. cm[/tex]
The sum of the perimeter of a square and the circumference of the circle is 80 cm
Let the radius of a circle be R cm.
Let the side of a square be A cm.
[tex] \sf \dashrightarrow Area \: of circle = 154[/tex]
[tex]\sf \dashrightarrow 22/7 × R × R = 154[/tex]
[tex] \sf \dashrightarrow R = 7 cm[/tex]
[tex]\boxed{\sf \: Circumference \: of \: a \: circle = 2πR}[/tex]
[tex]\sf \dashrightarrow 2 × 22/7 × 7 = 44 cm[/tex]
The sum of the perimeter of a square and circumference of a circle is 80 cm
[tex]\sf \dashrightarrow 4 × A + 44 = 80[/tex]
[tex]\sf \dashrightarrow 4A = 36[/tex]
[tex]\sf \dashrightarrow A = 9 cm[/tex]
[tex]\sf Side \: of \: square = 9 cm[/tex]
[tex]\boxed{\because\sf \: Diagonal \: of \: a \: square = 9 × √2 = 9√2 cm}[/tex]
[tex] \bf \: Additional \: Information[/tex]
[tex]\begin{gathered}\begin{gathered}\: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered} [/tex]
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Verified answer
[tex] \bf \: Given:[/tex]
[tex] \tt \: The \: area \: of \: the \: circle \: is \: 154 sq. cm[/tex]
The sum of the perimeter of a square and the circumference of the circle is 80 cm
[tex] \bf \: Formula \: Used:[/tex]
[tex] \tiny \bf \: Area \: of \: circle = πr {}^{2} [/tex]
[tex] \tt \tiny \: Circumference \: of \: a \: circle = 2πr[/tex]
[tex] \sf \tiny \: The perimeter \: of \: a \: square = 4 × side[/tex]
[tex] \bf \: Calculation:[/tex]
Let the radius of a circle be R cm.
Let the side of a square be A cm.
[tex] \sf \dashrightarrow Area \: of circle = 154[/tex]
[tex]\sf \dashrightarrow 22/7 × R × R = 154[/tex]
[tex] \sf \dashrightarrow R = 7 cm[/tex]
[tex]\boxed{\sf \: Circumference \: of \: a \: circle = 2πR}[/tex]
[tex]\sf \dashrightarrow 2 × 22/7 × 7 = 44 cm[/tex]
The sum of the perimeter of a square and circumference of a circle is 80 cm
[tex]\sf \dashrightarrow 4 × A + 44 = 80[/tex]
[tex]\sf \dashrightarrow 4A = 36[/tex]
[tex]\sf \dashrightarrow A = 9 cm[/tex]
[tex]\sf Side \: of \: square = 9 cm[/tex]
[tex]\boxed{\because\sf \: Diagonal \: of \: a \: square = 9 × √2 = 9√2 cm}[/tex]
[tex] \bf \: Additional \: Information[/tex]
[tex]\begin{gathered}\begin{gathered}\: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered} [/tex]