Question

Find a circumference of a base of cylinder if height is 10 cm and curved surface area is 400 cm square

Answer 1

Gɪᴠᴇɴ :-

• Height (h) = 10cm
• Curved Surface Area = 400 cm²

ᴛᴏ ғɪɴᴅ :-

• Circumference of Base

sᴏʟᴜᴛɪᴏɴ :-

We know that,

Circumference of Cylinder = 2πrh = 400

➭2πrh = 400

➭ πrh = 400/2

➭ πrh = 200

➭ πr×10 = 200

➭ πr = 200/10

➭ πr = 20

➭ r = 20 × 7/22

➭ r = 140/22

➭ r = 6.36 cm

Hence,

• Radius (r) = 6.3 cm

Now,

We know that,

• Circumference of Circle = 2πr

➭ 2πr = 2 × 22/7 × 6.3

➭ 2 × 22 × 0.9

➭ 44 × 0.9

➭ 39.6 cm ≈ 40cm

Hence,

• Circumference of a base of cylinder = 40 cm

Short Method :-

• Curved Surface area of Cylinder = Circumference of circle × Height

➠400 = 2πr × h

➠400 = 2πr × 10

➠ 2πr = 400/10

➠ 2πr = 40. --(1)

And,

• Circumference of Circle = 2πr

Hence,

➠ 2πr = 40. --(from -1)

Hence,

• Circumference of Base (Circle) = 40cm

Answer 2

Given,

height (h)=10cm

CSA=400cm

C.SA of cylinder = 2πrh

» 2πrh=400

» 2πr(10)=400

» 2πr = 40

circumference of base, 2πr=40cm.