Question

if the numerical values of volume and leteral surface area of a right circular cylinder and equal then find the radius of the cylinder ​

Answer 1

Step-by-step explanation:

Given :-

The numerical values of volume and lateral surface area of a right circular cylinder are equal.

To find :-

Radius of the cylinder

Solution :-

Let the radius of a right circular cylinder be r units

Let the height of the right circular cylinder be h units

We know that

Lateral Surface Area of a right circular cylinder (LSA) = 2πrh sq.units

and

Volume of a right circular cylinder (V)

= πr²h cubic. units

According to the given problem

Numerical values of LSA and Volume are equal

Volume of the cylinder = LSA of the cylinder

=> V = LSA

=> πr²h = 2πrh

On cancelling 'πh' both sides then

=> r² = 2r

=> r×r = 2×r

On cancelling 'r' both sides then

=> r = 2 units

Therefore, radius = 2 units

Answer :-

The radius of the given right circular cylinder is 2 units

Used formulae:-

→ Lateral Surface Area of a right circular cylinder (LSA) = 2πrh sq.units

→ Volume of a right circular cylinder (V)

= πr²h cubic. units

Where,

• r = radius
• h = height
• π = 22/7

Answer 2

Given Data :-

Volume and Lateral Surface area of a Right circular cylinder are numerically equal.

To Find :-

Radius of the Cylinder,(r)

Solution -

Volume (V) = πr²h

Lateral Surface Area (L.S.A) = 2πrh

so, V = LSA

⇒ πr²h = 2πrh

⇒ r² = 2r

⇒ r = 2 units

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FINAL ANSWER :

Radius of Cylinder (r) = 2 units.