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Answers
Answer:
Given :-
The lateral surface area of a cylinder is 132 cm² and its height is 7 cm.
To Find :-
What is the base diameter of a cylinder.
Formula Used :-
\clubsuit♣ Lateral Surface Area or Curved Surface Area Of Cylinder Formula :
\begin{gathered}\bigstar \: \: \sf\boxed{\bold{\pink{L.S.A_{(Cylinder)} =\: 2{\pi}rh}}}\: \: \: \bigstar\\\end{gathered}
★
L.S.A
(Cylinder)
=2πrh
★
where,
π = Pie or 22/7
r = Radius
h = Height
Solution :-
First, we have to find the radius of a cylinder :-
Given :
Height = 7 cm
Lateral Surface Area = 132 cm²
According to the question by using the formula we get,
\implies \bf L.S.A_{(Cylinder)} =\: 2{\pi}rh⟹L.S.A
(Cylinder)
=2πrh
\begin{gathered}\implies \sf 132 =\: 2 \times \dfrac{22}{7} \times r \times 7\\\end{gathered}
⟹132=2×
7
22
×r×7
\implies \sf 132 =\: \dfrac{44}{7} \times 7r⟹132=
7
44
×7r
\implies \sf 132 \times \dfrac{7}{44} =\: 7r⟹132×
44
7
=7r
\implies \sf \dfrac{\cancel{924}}{\cancel{44}} =\: 7r⟹
44
924
=7r
\implies \sf 21 =\: 7r⟹21=7r
\implies \sf \dfrac{\cancel{21}}{\cancel{7}} =\: r⟹
7
21
=r
\implies \sf 3 =\: r⟹3=r
\implies \sf\bold{\purple{r =\: 3\: cm}}⟹r=3cm
Now, we have to find the base diameter of a cylinder :
Given :
Radius = 3 cm
According to the question by using the formula we get,
\begin{gathered}\dashrightarrow \sf\boxed{\bold{\pink{Diameter =\: 2 \times Radius}}}\\\end{gathered}
⇢
Diameter=2×Radius
\dashrightarrow \sf Diameter =\: 2 \times 3\: cm⇢Diameter=2×3cm
\dashrightarrow \sf\bold{\red{Diameter =\: 6\: cm}}⇢Diameter=6cm
\therefore∴ The base diameter of a cylinder is 6 cm .