Question

a cylinder has a radius 7 cm and height 14 cm .Find its lateral surface area wnd total surface area​

Answer 1

EXPLANATION.

Radius of the cylinder = 7 cm.

Height of the cylinder = 14 cm.

As we know that,

Formula of :

Lateral surface area of cylinder = 2πrh.

Total surface area of cylinder = 2πr(r + h).

Using this formula in the equation, we get.

Lateral surface area of cylinder = 2πrh.

⇒ 2 x 22/7 x 7 x 14.

⇒ 2 x 22 x 14 = 616 cm².

Total surface area of cylinder = 2πr(r + h).

⇒ 2 x 22/7 x 7 x (7 + 14).

⇒ 2 x 22 x (21) = 924 cm².

Lateral surface area of cylinder = 616 cm².

Total surface area of cylinder = 924 cm².

                                                                                                                     

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 sphere = 4/3πr³.

(6) Volume of hemisphere = 2/3πr³.

Answer 2

Answer:

Given :-

• A cylinder has a radius of 7 cm and height is 14 cm.

To Find :-

• What is the lateral surface area and total surface area of a cylinder.

Formula Used :-

$\clubsuit$ Lateral Surface Area or Curved Surface Area of Cylinder :

$\bigstar \: \: \sf\boxed{\bold{\pink{Lateral\: Surface\: Area_{(Cylinder)} =\: 2{\pi}rh}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

$\clubsuit$ Total Surface Area or T.S.A of Cylinder Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{T.S.A_{(Cylinder)} =\: 2{\pi}r(h + r)}}}\: \: \: \bigstar$

where,

• T.S.A = Total Surface Area
• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

$\sf\bold{\underline{\purple{\clubsuit\: In\: case\: of\: lateral\: surface\: area\: of\: cylinder\: :-}}}$

Given :

• Radius = 7 cm
• Height = 14 cm

According to the question by using the formula we get,

$\implies \sf Lateral\: Surface\: Area_{(Cylinder)} =\: 2 \times \dfrac{22}{7} \times 7 \times 14$

$\implies \sf Lateral\: Surface\: Area_{(Cylinder)} =\: \dfrac{44}{7} \times 98$

$\implies \sf Lateral\: Surface\: Area_{(Cylinder)} =\: \dfrac{\cancel{4312}}{\cancel{7}}$

$\implies \sf\bold{\red{Lateral\: Surface\: Area_{(Cylinder)} =\: 616\: cm^2}}$

$\therefore$ The lateral surface area of a cylinder is 616 cm² .

━━━━━━━━━━━━━━━━━━━━━━━

$\sf\bold{\underline{\purple{\clubsuit\: In\: case\: of\: total\: surface\: area\: of\: cylinder\: :-}}}$

Given :

• Radius = 7 cm
• Height = 14 cm

According to the question by using the formula we get,

$\implies \sf T.S.A_{(Cylinder)} =\: 2 \times \dfrac{22}{7} \times 7(14 + 7)$

$\implies \sf T.S.A_{(Cylinder)} =\: \dfrac{44}{7} \times 7(21)$

$\implies \sf T.S.A_{(Cylinder)} =\: \dfrac{44}{7} \times 147$

$\implies \sf T.S.A_{(Cylinder)} =\: \dfrac{\cancel{6468}}{\cancel{7}}$

$\implies \sf\bold{\red{T.S.A_{(Cylinder)} =\: 924\: cm^2}}$

$\therefore$ The total surface area of a cylinder is 924 cm² .