Question

The total surface area of cylinder is 446 .The curve surface area is one third total surface area .Find the volume of cylinder

Answer 1

Answer:

• Volume of cylinder = 511.28 cm³ (Approx)

Step-by-step explanation:

Given:

• TSA of Cylinder = 446 cm²
• CSA = 1/3 × TSA

To Find:

• Volume of cylinder

Now, we know that

⇒ TSA of cylinder = 446 cm²

⇒ 2πrh + 2πr² = 446 cm²       ..........(1)

And,

⇒ CSA of cylinder = 1/3 × TSA

⇒ 2πrh = 1/3 × 446

⇒ 2πrh = 148.66 cm²       ...........(2)

Now, put the value of 2πrh in Equation (1), we get

⇒ 2πrh + 2πr² = 446 cm²

⇒ 148.66 + 2πr² = 446

⇒ 2πr² = 446 - 148.66

⇒ 2πr² = 297.34

⇒ 6.28r² = 297.34

⇒ r² = 297.34/6.28

⇒ r² = 47.34

⇒ r = √47.34

⇒ r = 6.88

Now, put the value of 'r' in Equation (2), we get

⇒ 2πrh = 148.66 cm²

⇒ 2 × 3.14 × 6.88 × h = 148.66

⇒ 43.20 × h = 148.66

⇒ h = 148.66/43.20

⇒ h = 3.44

Now, we know that,

⇒ Volume of cylinder = πr²h

⇒ Volume of cylinder = 3.14 × 6.88 × 6.88 × 3.44

⇒ Volume of cylinder = 511.28 cm³ (Approx)

Hence, Volume of cylinder = 511.28 cm³ (Approx)