Question

The curved surface area of a cylinder is 4400 cm ^2 and the circumference of its base is 110 cm . Find the height and the volume of the cylinder .

Answer 1

$\Large{\underline{\underline{\bf{\red{Given}}}}}$

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm .

$\Large{\underline{\underline{\bf{\red{Find\:out}}}}}$

Find the height and the volume of the cylinder .

$\Large{\underline{\underline{\bf{\red{Solution}}}}}$

• Circumference of cylinder = 110cm

★ Let the radius be " r "

➞ 2πr = 110

➞ 2 × 22/7 × r = 110

➞ 44/7 × r = 110

➞ r = 7 × 110/44

➞ r = 17.5 cm

__________________________

• C.S.A of cylinder = 4400

★ Let the height of cylinder be " h "

➞ 2πrh = 4400

➞ circumference of cylinder × height = 4400

➞ 110 × h = 4400

➞ h = 4400/110

➞ h = 40 cm

___________________________

Now volume of cylinder

➞ πr² h

➞ 22/7 × 17.5 × 17.5 × 40

➞ 22 × 2.5 × 17.5 × 40

➞ 38500 cm³

$\large{\underline{\boxed{\bf{\purple{Volume\:of\: cylinder=38500cm^3}}}}}$

Answer 2

Gɪᴠᴇɴ :-

Cylinder:-

• Curved Surface Area = 4400 cm²
• Circumference of Base = 110 cm

ᴛᴏ ғɪɴᴅ :-

Cylinder :-

• Height (h)
• Volume (V)

sᴏʟᴜᴛɪᴏɴ :-

We know that,

Circumference of circle = 2πr = 110

➭2πr = 110

➭ πr = 110/2

➭ πr = 55

➭ r = 55 × 7/22

➭ r = 35/2

➭ r = 17.5 cm

Hence,

• Radius (r) = 17.5 cm

Now,

We know that,

Curved surface area of cylinder = 2πrh = 4400

➭ 2πrh = 4400

➭ πrh = 4400/2

➭ πrh = 2200

➭ 22/7 × 17.5 × h = 2200

➭ 22 × 2.5 × h = 2200

➭ 55h = 2200

➭ h = 2200/55

➭ h = 40 cm

Hence,

• Height (h) = 40 cm

Now

We know that,

Volume of Cylinder = πr²h

➭ πr²h = 22/7 × (17.5)² × 40

➭ 22/7 × 306.25 × 40

➭ 22 × 43.75 × 40

➭ 962.5 × 40

➭ 38500 cm³

Hence,

• Volume (V) = 38500 cm³