Question

The volume of a cylinder is 150pie cube cm and its height is 6cm . Find the areas of its total surface and lateral(curved) surface.​

Answer 1

Given :-

• The volume of a cylinder is 150pie cube cm and its height is 6cm.

To find :-

• Total surface area and lateral surface area

Solution :-

• Volume of cylinder = 150π

• Height of cylinder = 6cm

✚To find total surface area or curved surface area of cylinder, firstly we have to find out radius of cylinder.

As we know that

Volume of cylinder = πr²h

→ 150π = πr²h

Cancel π in both side i.e LHS (left hand side and RHS (right hand side)

→ 150 = r²h

→ 150 = r² × 6

→ r² = 150/6

→ r² = 25

→ r = √25

→ r = ± 5

• Note : Radius never in negative
• Take 5cm as a radius

So, radius of cylinder is 5cm

Now, lateral surface area of cylinder

→ 2πrh

✚Put the values of radius and height

→ 2 × 22/7 × 5 × 6

→ 44/7 × 30

→ 1320/7

→ 188.57 cm²

Total surface area of cylinder

→ Curved surface area of cylinder + 2 × base area of cylinder

→ 2πrh + 2πr²

Take 2πr as a common

→ 2πr(h + r)

→ 2 × 22/7 × 5(6 + 5)

→ 44/7 × 5 × 11

→ 2420/7

→ 345.71 cm²

We can also find out total surface area by substituting the value of curved surface area

→ 2πrh + 2πr²

→ 188.57 + 2 × 22/7 × (5)²

→ 188.57 + 44/7 × 25

→ 188.57 + 1100/7

→ 188.57 + 157.14

→ 345.71 cm²

Hence,

• Curved surface area of cylinder = 188.57cm²

• Total surface area of cylinder = 345.71cm²