Question

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. (Assume π =22/7 )​

Answer 1

Step-by-step explanation:

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The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.

Solution:

Let the radius and height of the cylinder be 'r' and 'h' respectively.

Curved Surface Area of a right circular cylinder = 2 π r h

Diameter = 2 × radius

Height of the cylinder, h = 14 cm

CSA of the cylinder = 88 cm²

2 π r h = 88 cm²

2 × 22/7 × r × 14 cm = 88 cm²

r = (88 cm² × 7) / (2 × 22 × 14) cm

= 1 cm

Diameter = 2 × radius

= 2 × 1 cm

= 2 cm

Thus, the diameter of the base of the cylinder is 2 cm.

Answer 2

C O N C E P T :

• we have found the value of radius of cylinder by equating the value of curved surface area of cylinder and its formula from there we get the value of radius then we find the value of diameter.

G I V E N :

• The Height of Cylinder = 14 cm

• and curved surface area of cylinder = 88 cm²

• Also curved surface area = 2 πrh

T O F I N D :

• The diameter of the base of the cylinder.

F O R M U L A U S E D :

• The curved surface area of cylinder = 2πrh

S O L U T I O N

From this we can find the value of ‘r’ and by finding the value of ‘r’ we can determine the diameter of the cylinder

: $\implies$ r = 88 / 2πh

: $\implies$ Or r = 44 / π × 14

: $\implies$ or = 22 / π × 7

: $\implies$ or r = 22 / π × 7

: $\implies$ or r = 1 cm { ∴ π = 22 / 7 }

: $\implies$ Now diameter of the base = 2r

: $\implies$ 2 r = 2 × 1 = 2 cm

F I N A L A N S W E R :

Hence, the diameter of the base of the cylinder is 2 cm