A solid is in the form of a right circular cylinder, with a hemisphere

1.	A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm, respectively. Find the total surface area of the solid.( use π = \(\frac{22}7\))
Answer» Height of cylinder (h) = 10 cm Height of conical part = 6 cm Slant height of cone (l) = \(\sqrt{r^2 + h^2}\) ⇒ l = \(\sqrt{3.5^2 + 6^2}\) ⇒ l = 48.25 cm Curved surface area of cone = πrl = π (3.5) (48.25) = 76.408 cm² …(1) Curved surface area of cylinder = 2πrh = 2π (3.5) (10) = 220 cm²…(2) Curved surface area of hemisphere = 2πr² = 2π (3.5)² = 77 cm² ….(3) ∴ Total curved surface area = Curved surface area of(cone + cylinder + hemisphere) = 76.408 + 220 + 77 = 373.408 ∴ Total surface area of solid = 373.408 cm²

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm, respectively. Find the total surface area of the solid.( use π = \(\frac{22}7\))

Answer»

Height of cylinder (h) = 10 cm

Height of conical part = 6 cm

Slant height of cone (l) = \(\sqrt{r^2 + h^2}\)

⇒ l = \(\sqrt{3.5^2 + 6^2}\)

⇒ l = 48.25 cm

Curved surface area of cone = πrl

= π (3.5) (48.25)

= 76.408 cm² …(1)

Curved surface area of cylinder = 2πrh

= 2π (3.5) (10)

= 220 cm²…(2)

Curved surface area of hemisphere = 2πr²

= 2π (3.5)²

= 77 cm² ….(3)

∴ Total curved surface area = Curved surface area of(cone + cylinder + hemisphere)

= 76.408 + 220 + 77

= 373.408

∴ Total surface area of solid = 373.408 cm²