. 3. Short Answer type questions (SA): (i) If the numerical values of volume and lateral surface area of a right circular cylinder are equal then find the radius of the cylinder.
Answers
Given :
The numerical values of volume and lateral surface area of a right circular cylinder are equal
- As we know that
• Volume of cylinder = πr²h
• Lateral surface area of cylinder = 2πrh
According to the given condition, both volume and lateral surface area are equal.
•°• πr²h = 2πrh
- Cancel π, r and h
→ r = 2
Hence, the required value of radius is 2 unit
➥ Given :
The numerical values of volume and lateral surface area of a right circular cylinder are equal
➥To Find :
- ➻ Find the radius of the cylinder
➥ Explanation :
Assume that h and r be the height and radius of the base of right circular cylinder.
As we know that
- ➻ Curved surface area of cylinder = 2πrh,
where 'r' is the radius of the base and 'h' is the height of the cylinder.
The formula for the volume surface area of a cylinder is V=Bh or V=πr²h
where 'r' is the radius of the base and 'h' is the height of the cylinder
➥ Now :-
We have
- ➻ surface Area = Volume
➥ So
- ➻ 2 π rh = πr²h
The π rh get eliminated now we have
- ➻ r = 2 units
➥Therefore,
The radius of Cylinder is 2 units