Question

Classify the given pairs of sets as disjoint, overlapping, equal or equivalent sets:
i) set X = {/ ℎ 8}
set Y = {/ ℎ 8}
ii) set M = {/ ℎ }
set N = {/ ∈ , −4 < < 2}
iii) set A = {, ,,}
set B = {, , ,}

Answer 1

Answer:

Appropriate Question :-

The curved surface area of a hollow cylinder is 4375 sq. meter. It is cut along its height and formed a rectangular sheet of width 35 m. Find perimeter of rectangular sheet.

\large\underline{\sf{Solution-}}

Solution−

Given that,

The curved surface area of a hollow cylinder is 4375 sq. meter. It is cut along its height and formed a rectangular sheet of width 35 m.

Let assume that length of rectangular sheet be x m.

So, According to given question,

\begin{gathered}\rm\implies \:CSA_{(cylinder)} = Area_{(rectangle)} \\ \end{gathered}

⟹CSA

(cylinder)

=Area

(rectangle)

\begin{gathered}\rm \: 4375 = Length \times width \\ \end{gathered}

4375=Length×width

\begin{gathered}\rm \: 4375 = x \times 35 \\ \end{gathered}

4375=x×35

\begin{gathered}\rm \: x = \dfrac{4375}{35} \\ \end{gathered}

x=

35

4375

\begin{gathered}\rm\implies \:x \: = \: 125 \\ \end{gathered}

⟹x=125

\begin{gathered}\rm\implies \:Length_{(rectangle)} \: = \: 125 \: m \\ \end{gathered}

⟹Length

(rectangle)

=125m

Now, we have

\begin{gathered}\rm \: Length_{(rectangle)} \: = \: 125 \: m \\ \end{gathered}

Length

(rectangle)

=125m

\begin{gathered}\rm \: Width_{(rectangle)} \: = \: 35 \: m \\ \end{gathered}

Width

(rectangle)

=35m

Now,

\begin{gathered}\rm \: Perimeter_{(rectangle)} \\ \end{gathered}

Perimeter

(rectangle)

\begin{gathered}\rm \: = \: \: \: 2\bigg(Length_{(rectangle)} + Width_{(rectangle)}\bigg) \\ \end{gathered}

= 2(Length

(rectangle)

+Width

(rectangle)

)

\begin{gathered}\rm \: = \: \: \: \: 2(125 + 35) \: \\ \end{gathered}

= 2(125+35)

\begin{gathered}\rm \: = \: \: \: \: 2 \times 160 \\ \end{gathered}

= 2×160

\begin{gathered}\rm \: = \: \: \: \: 320 \: m \\ \end{gathered}

= 320m

Thus,

\begin{gathered}\rm\implies \:Perimeter_{(rectangle)} \: = \: 320 \: m \\ \end{gathered}

⟹Perimeter

(rectangle)

=320m

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information :-

\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}

†

FormulasofAreas:−

⋆Square=(side)

2

⋆Rectangle=Length×Breadth

⋆Triangle=

2

1

×Base×Height

⋆Scalene△=

s(s−a)(s−b)(s−c)

⋆Rhombus=

2

1

×d

1

×d

2

⋆Rhombus=

2

1

d

4a

2

−d

2

⋆Parallelogram=Base×Height

⋆Trapezium=

2

1

(a+b)×Height

⋆EquilateralTriangle=

4

3

(side)

2