Question

CSA of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.
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Answer 1

Given :

• Height of Cylinder is 14 cm .
• C.S.A of Cylinder is 88 cm² .

To Find :

• Diameter of the base .

Solution :

$\longmapsto\tt{Height=14\:cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\:pi{rh}}$

Putting Values :

$\longmapsto\tt{88=2\times\dfrac{22}{{\cancel{7}}}\times{r}\times{{\cancel{14}}}}$

$\longmapsto\tt{88=44\times{2}\times{r}}$

$\longmapsto\tt{88=88r}$

$\longmapsto\tt{r=\cancel\dfrac{88}{88}}$

$\longmapsto\tt\bf{r=1\:cm}$

As we know that Diameter is double of Radius . So ,

$\longmapsto\tt{Diamtere=2r}$

$\longmapsto\tt{2(1)}$

$\longmapsto\tt\bf{2\:cm}$

So , The Diameter of the base of Cylinder is 2 cm .

Answer 2

Given information,

CSA of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.

• Height of cylinder = 14 cm
• CSA of cylinder = 88 cm²
• Diameter of base of cylinder = ?

Using formula,

✪ CSA of cylinder = 2πrh ✪

Where,

• π = Pi
• r = radius of base of cylinder
• h = height of cylinder

We have,

• π = 22/7
• r = ?
• h = 14 cm
• CSA of cylinder = 88 cm²

Putting all values,

➻ 88 = 2 × 22/7 × r × 14

➻ 88 = 2 × 22 × r × 2

➻ 88 = 2 × 22 × 2 × r

➻ 88 = 88 × r

➻ 88 = 88r

➻ r = 88/88

➻ r = 1

• Henceforth, radius of base of right cylinder is 2 cm.

Now,

• We know that •

✪ Diameter = Radius × 2 ✪

Putting all values,

◐ Diameter = r × 2

◐ Diameter = 1 × 2

◐ Diameter = 2 cm

• Henceforth, diameter of base of right circular cylinder is 2 cm.

Verification,

➻ CSA of cylinder = 2πrh

➻ 88 = 2 × 22/7 × 1 × 14

➻ 88 = 2 × 22 × 2

➻ 88 = 22 × 4

➻ 88 = 88

➻ LHS = RHS

Hence, Verified ✔

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