Question

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

Answer 1

⇝Given :-

• Curved Surface area = 88 cm²
• Height = 14 cm

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⇝To Find :-

• Base = ?

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⇝Solution :-

❒ We know that :

${\large{\red{\bigstar \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{CSA = 2πrh}}}}}}}}}$

❒ Here :

• CSA = Curved Surface area = 88cm²
• π = pi = 22/7
• H = Height = 14cm
• R = ?

❒ Curved Surface area :

${\large{:{\longmapsto{\text{CSA =2πrh}}}}}$

${\large{:{\longmapsto{\bf{88 {cm}^{2} = 2 \times \frac{22}{7} \times r \times 14}}}}}$

${\large{:{\longmapsto{\bf{88cm = \frac{44}{7} \times r \times 14}}}}}$

${\large{:{\longmapsto{\bf{88cm = {\cancel\frac{616}{7}} \times r }}}}}$

${\large{:{\longmapsto{\bf{88cm = 88 \times r }}}}}$

${\large{:{\longmapsto{\bf{R = {\cancel\frac{88}{88} } }}}}}$

${\large{\red{:{\twoheadrightarrow{\purple{\underline{\boxed{\bf{Radius = 1cm}}}}}}}}}$

❒ Than Diameter :

${\large{\red{\bigstar \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{Diameter = 2 \times Radius}}}}}}}}}$

${\large{:{\longmapsto{\bf{Diameter = 2 \times Radius}}}}}$

${\large{:{\longmapsto{\bf{Diameter = 2 \times 1}}}}}$

${\large{\red{:{\twoheadrightarrow{\purple{\underline{\boxed{\bf{Radius = 2cm}}}}}}}}}$

❒ Hence :

Diameter of the cylinder is 2cm.

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Answer 2

Answer:

• Diameter of base of cylinder = 2 cm.

Explanation:

Given information,

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

• Height of cylinder = 14 cm
• C.S.A of cylinder = 88 sq.cm
• Diameter of base of cylinder = ?

Using formula,

✪ C.S.A 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
• C.S.A of cylinder = 88 sq.cm

Putting all values,

➻ 88 = 2 × 22/7 × r × 14

➻ 88 = 2 × 22 × r × 2

➻ 88 = 2 × 22 × 2 × r

➻ 88 = 44 × 2 × r

➻ 88 = 88 × r

➻ 88 = 88r

➻ r = 88/88

➻ r = 1/1

➻ r = 1

• Henceforth, radius of base of right circular cylinder is 1 cm.

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:

➻ C.S.A of cylinder = 2πrh

Putting all values,

➻ 88 = 2 × 22/7 × 1 × 14

➻ 88 = 2 × 22 × 1 × 2

➻ 88 = 2 × 22 × 2

➻ 88 = 44 × 2

➻ 88 = 88

➻ LHS = RHS

Hence, Verified ✔

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