Question

if the lateral surface are of a cylinder 132cm² and its height is 7cm, then its base diameter is..I want step by step explanation​

Answer 1

EXPLANATION.

Lateral surface area of a cylinder = 132 cm².

Height = 7 cm.

As we know that,

Formula of :

Lateral surface area of cylinder = 2πrh.

Using this formula in the equation, we get.

⇒ 2 x 22/7 x r x 7 = 132.

⇒ 2 x 22 x r = 132.

⇒ 22 x r = 66.

⇒ r = 3 cm.

Radius of cylinder = 3 cm.

Diameter = 2 x Radius.

Diameter of base of cylinder = 2 x 3 = 6 cm.

                                                                                                                       

MORE INFORMATION.

(1) Volume of cuboid = L x B x H.

(2) Volume of cube = a³.

(3) Volume of cylinder = πr²h.

(4) Volume of cone = 1/3πr²h.

(5) Volume of hemisphere = 2/3πr³.

(6) Volume of sphere = 4/3πr³.

Answer 2

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 :

$\bigstar \: \: \sf\boxed{\bold{\pink{L.S.A_{(Cylinder)} =\: 2{\pi}rh}}}\: \: \: \bigstar$

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,

$\implies \bf L.S.A_{(Cylinder)} =\: 2{\pi}rh$

$\implies \sf 132 =\: 2 \times \dfrac{22}{7} \times r \times 7$

$\implies \sf 132 =\: \dfrac{44}{7} \times 7r$

$\implies \sf 132 \times \dfrac{7}{44} =\: 7r$

$\implies \sf \dfrac{\cancel{924}}{\cancel{44}} =\: 7r$

$\implies \sf 21 =\: 7r$

$\implies \sf \dfrac{\cancel{21}}{\cancel{7}} =\: r$

$\implies \sf 3 =\: r$

$\implies \sf\bold{\purple{r =\: 3\: cm}}$

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,

$\dashrightarrow \sf\boxed{\bold{\pink{Diameter =\: 2 \times Radius}}}$

$\dashrightarrow \sf Diameter =\: 2 \times 3\: cm$

$\dashrightarrow \sf\bold{\red{Diameter =\: 6\: cm}}$

$\therefore$ The base diameter of a cylinder is 6 cm .