From a solid cylinder whose height is 2.8 cm and radius 2.1 cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total surface area of the remaining solid.

 From a solid cylinder whose height is 2.8 cm and radius 2.1 cm, a conical cavity of the same height and same radius is hollowed out. Find the volume and the total surface area of the remaining solid.

Cylinder and conical cavity have same radius and height

r = 2.1 cm, h = 2.8 cm

.Volume of remaining solid

 Volume of cylinder − Volume of cone 

Volume of cylinder = πr²h = π × (2.1)² × 2.8 = π × 4.41 × 2.8 = 12.348π cm³  

Volume of cone = (1/3)πr²h = (1/3) × 12.348π = 4.116π cm³

Remaining volume = 12.348π − 4.116π = 8.232π cm³  

Using π = 22/7

Remaining volume  = 8.232 × 22/7 = 25.872 cm³ ≈ 25.87 cm³

. Total surface area of remaining solid

Surfaces left after hollowing:  

Bottom circular base of cylinder = πr²  

Curved surface of cylinder = 2πrh  

Curved surface of cone = πrl  

Slant height of cone: l = √(r² + h²) = √(2.1² + 2.8²) = √(4.41 + 7.84) = √12.25 = 3.5 cm 

Required surface area = πr² + 2πrh + πrl

 = π(2.1)² + 2π(2.1)(2.8) + π(2.1)(3.5)

 = 4.41π + 11.76π + 7.35π = 23.52π cm²  Using π = 22/7:

 = 23.52 × 22/7 = 73.92 cm²  

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mensuration,   surface area and volume of solids , cbse th maths old board exam question paper 2025 2026