Question

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

Answer 1

$\large\underline\pink{Given:-}$

• Curved surface area of cylinder = 88 cm²
• Cylinder of Height = 14 cm

$\large\underline\pink{To find:-}$

• Fine the diameter of the base of the cylinder ....?

$\large\underline\pink{Solutions:-}$

$\: \: \: \: \: \therefore \: \: Curved \: \: surface \: \: area \: \: of Cylinder \: \: = \: \: {2} \: \pi \: r \: h$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {r} \: \times \: {14} \: \: = \: \: {88}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {r} \: \times \: {2} \: \: = \: \: {88}$

$\: \: \: \: \: \leadsto \: \: {88} \: \times \: {r} \: \: = \: \: {88}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: \frac{88}{88}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {1}$

Now, The diameter of the base of the cylinder is 2r.

⟹ 2 × 1

⟹ 2 cm.

$\: \: \: \: \: \: \: Hence, \\ \: \:\therefore \: \: The \: \: diameter \: \: of \: \: a \: \: cylinder \: \: {2} \: cm.$

$\large\underline\pink{More \: Information:-}$

• Volume of cylinder ( Area of base × height ).

= (πr²) × h

= πr²h

• Curved surface = ( Perimeter of base ) × height.

= (2πr) × h

= πrh

• Total surface are = Area of circular ends + curved surface area.

= 2πr² + 2πrh

= 2πr(r + h)

Where, r = radius of the circular base of the cylinder.

h = height of cylinder.

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Answer 2

Required Answer:

GiveN:

Curved surface of the cylinder is 88 cm

Height of the cylinder = 14 cm

To FinD:

Diameter of the base?

Step-by-step Explanation:

Curved surface area of cylinder can be determined by:

$\large{ \boxed{ \rm{CSA = 2\pi rh}}}$

Here, r is the radius of the base and h is the height of the cylinder.

Now putting the values to get the radius first,

⇒ 2πrh = CSA

⇒ 2 × 22/7 × r × 14 cm = 88 cm²

⇒ 88r cm = 88 cm²

⇒ r = 1 cm

Then, Diameter of the cylinder:

= 2 × Radius

= 2 × 1 cm

= 2 cm

Hence,

The diameter of the base of the cylinder is 2 cm (Ans)