Given:

✰ Total surface area of cylinder (T.S.A) = 4144.80 cm²

✰ Height of cylinder (h) = 13 cm

To find:

✠ Curved surface area (C.S.A) of cylinder.

✠ Volume ( V ) of cylinder.

Solution:

Let's understand the concept first! We will find out the radius of a circle by using formula to calculate total surface PUTTING, the values in the formula and then doing the required calculations. After FINDING out the radius of a circle, we will use formula of curved surface area and volume respectively to find them.

Let's find out...!

✭ Total surface area (T.S.A) = 2πR (h + r) ✭

Where,

• r is the radius of the cylinder.
• h is the the height of the cylinder.

Putting the values in the formula, we have:

➛ 4144.80 = 2 × 22/7 × r ( 13 + r )

➛ 4144.80 = 2 × 22/7 × 13r + r²

➛ 4144.80 = 44/7 × 13r + r²

➛ 13r + r² = 4144.80 × 7/44

➛ 13r + r² = 659.4

➛ r + r² = 659.4/13

➛ 2r² = 50.7231

➛ r² = 50.7231/2

➛ r² = 25.4

➛ r = √25.4

➛ r ≈ 5.04 cm

Now,

✭ Curved surface area (C.S.A) = 2πrh ✭

Where,

• r is the radius of the cylinder.
• h is the the height of the cylinder.

Putting the values in the formula, we have:

➤ Curved surface area (C.S.A) = 2 × 22/7 × 5.04 × 13

➤ Curved surface area (C.S.A) = 2 × 22/7 × 65.52

➤ Curved surface area (C.S.A) = 44/7 × 65.52

➤ Curved surface area (C.S.A) = 2882.88/7

➤ Curved surface area (C.S.A) = 411.84 cm²

∴ Curved surface area (C.S.A) of cylinder = 411.84 cm²

✭ Volume ( V ) of cylinder = πr²h ✭

Where,

• r is the radius of the cylinder.
• h is the the height of the cylinder.

Putting the values in the formula, we have:

➤ Volume ( V ) of cylinder = 22/7 × 25.4 × 13

➤ Volume ( V ) of cylinder = 22/7 × 330.2

➤ Volume ( V ) of cylinder = 7264.4/7

➤ Volume ( V ) of cylinder ≈ 1037.8 cm³

∴ Volume ( V ) of cylinder = 1037.8 cm³

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