Question

A solid cylinder has a total surface area of 231 cm^2. Its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.

NOTE: PLZ ANSWER QUICK NEED IT URGENTLY WITH THE PROCEEDURE

PLZ DON'T GIVE WRONG ANSWER

Answer 1

Given

TSA of cylinder = 232 cm²

CSA of cylinder = ⅔ of TSA

To find

Volume of cylinder

Solution

As we know,

➥ CSA of cylinder = 2πrh

Now, CSA of cylinder = TSA of cylinder

And, TSA = 231 cm²

⇰ CSA of cylinder = ⅔ of 231

⇰ CSA of cylinder = 77 × 2

⇰ CSA of cylinder = 154 cm²

We know that,

➥ TSA of cylinder = 2πr(r + h)

➙ 231 = 2πr² + 2πrh

➙ 231 = 2 × 22/7 × r² + 154

➙ 231 - 154 = (44/7) r²

➙ 77 = 44r²/7

➙ r² = 77 × 7/44

➙ r² = 12.25

➙ r = √12.25

➙ r = 3.5 cm

According to Question :

⟼ 2πrh = 154

⟼ 2 × 22/7 × rh = 154

⟼ 44/7 × rh = 154

⟼ rh = 154 × 7/44

⟼ rh = 7 × 3.5

⟼ rh = 24.5 cm. -(eq.1)

We know that,

➥ Volume of cylinder = πr²h

Putting all values :

➻ Volume of cylinder = 22/7 × rh × r

➻ Volume of cylinder = 22/7 × 24.5 × r

➻ Volume of cylinder = 77 × 3.5

➻ Volume of cylinder = 269.5 cm³

Therefore,

Volume of cylinder = 269.5 cm³

Answer 2

Given :-

• TSA of cylinder = 231cm².
• CSA of cylinder = (2/3) of TSA .

To Find :-

• Volume of Cylinder ?

Formula used :-

• CSA of cylinder = 2 * π * r * h
• TSA of cylinder = CSA + 2πr² = 2πrh + 2πr²
• Volume of Cylinder = π * r² * h

Solution :-

⟼ CSA = (2/3) * TSA

⟼ CSA / TSA = 2/3

Putting values we get,

⟼ (2πrh)/[2πr(h + r)] = 2/3

⟼ h/(h + r) = 2/3

⟼ 3h = 2h + 2r

⟼ 3h - 2h = 2r

⟼ h = 2r

_______________

Putting value of h = 2r in given TSA now, we get,

⟿ 2πr(2r + r) = 231

⟿ 2πr * 3r = 231

⟿ 2 * (22/7) * 3r² = 231

⟿ 2 * 2 * 3r² = 21*7

⟿ 4r² = 7*7

⟿ r² = (49/4)

⟿ r² = (7/2)²

⟿ r = (7/2) cm.

Hence,

⟿ h = 2r = 2*(7/2) = 7cm.

________________

Therefore,

➪ V = π * r² * h

➪ V = (22/7) * (7/2)² * 7

➪ V = ( 11 * 7 * 7 ) / 2

➪ V = (539/2)

➪ V = 269.5cm³. (Ans.)

Hence, Volume of Required Cube will be 269.5cm³.