From a solid cylinder of height 4 cm and radius 3 cm a conical cavity of height 4 cm and of base rad...........

Quantitative Aptitude ( CCS) Mensuration 3D

From a solid cylinder of height 4 cm and radius 3 cm, a conical cavity of height 4 cm and of base radius 3 cm is hollowed out. What is the total surface area of the remaining solid ?

15π sq cm

22π sq cm

33π sq cm

48π sq cm

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Explanation:

Given, height of cylinder (h₁) = 4 cm and height of cone (h₂) = 4 cm
And, radius of cylinder (r₁) = 3 cm and radius of cone (r₂) = 3 cm
∴ Total surface area of the remaining solid = Curved surface area of cylinder + Curved surface area of cone + Surface area of top of cylinder
= 2πr₁h₁ + πr₂l + πr₁²
= π(2r₁h₁ + r₂l + r₁²)
= π(2 × 3 × 4 + 3√3² + 4² + 3²)
= π(24 + 15 + 9) = 48π sq cm