From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. Take =22/7 if base circumference of cylinder is 2.8 cm find the radius of cylinder
Answers
Answer:
Height of solid cylinder = h = 2.8 cm
Diameter of solid cylinder = 4.2 cm
Radius of solid cylinder = r = Diameter ÷ 2 = 2.1 cm
Curved Surface area of solid cylinder = 2πrh
= 2 × 22/7 × 2.1 × 2.8 cm2
= 2 × 22/7 × 2.1 × 2.8 cm2
= 36.96 cm2
Height of conical cavity = h = 2.8 cm
Radius conical cavity = r = 2.1 cm
Let l be the slant height of conical cavity
l2 = r2 + h2
⇒ l2 = (2.82 + 2.12) cm2
⇒ l2 = (7.84 + 4.41) cm2
⇒ l2 = 12.25 cm2
⇒ l = 3.5 cm
Curved Surface area of conical cavity = πrl
= 22/7 × 2.1 × 3.5
= 23.1 cm2
Total surface area of remaining solid = Curved surface area of solid cylinder + Curved surface area of conical cavity + Area of circular base
Total surface area of remaining solid = (36.96 + 23.1 + 22/7 × 2.12) cm2
= (36.96 + 23.1 + 13.86) cm2
= 73.92 cm2