Question

the volume of a cylinder is 150cu.cm and its height is 6 cm . find the area of its total surface area and lateral surface area.​

Answer 1

Answer:

csa = 3600π

tsa= 183600π

Answer 2

Given:

• Volume = 150 cm³
• Height = 6 cm

To find:

➪ Total Surface Area = ?

➪ Lateral Surface Area = ?

Method:

Formula used:

Volume = r² h

⇒ 150 = r² × 6

Cancelling on both sides.

150 = r² × 6

⇒ r² = 25

⇒ r = √25

⇒ r = ± 5

Radius cannot be negative.

∴ r = 5 cm

Now let's find TSA and LSA

Total Surface Area = 2 r(r + h)

$\implies \sf{Total\:Surface\:Area = 2 \times \dfrac{22}{7} \times 5 (5+6)}\\\\\\\\\implies \sf{Total\:Surface\:Area = 2 \times \dfrac{22}{7} \times 5 \times 11}\\\\\\\\\implies \sf{Total\:Surface\:Area = \dfrac{44 \times 55}{7}}\\\\\\\\\implies \boxed{\bf{Total\: Surface\: Area = 345.71 cm^{2} }}$

$\sf{Lateral\: Surface\: Area = 2 \pi r h}\\\\\\\implies \sf{Lateral\: Surface\: Area = 2 \times \dfrac{22}{7} \times 5 \times 6}\\\\\\\implies \boxed{\bf{Lateral\: Surface\: Area = 188.57 cm^{2} }}$