Question

A solid toy in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. Also find the surface area of the toy.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Volume = 25.14 cm³

Surface area = 42.92 cm²

Step-by-step explanation:

Find the radius:

Radius = Diameter ÷ 2

Radius = 4 ÷ 2 = 2 cm

Find the volume of the hemisphere:

Volume of the hemisphere = 2/3πr³

Volume = 2/3 π (2)³ = 16π/3 cm³

Find the volume of the circular cone:

Volume of the cone = 1/3 πr²h

Volume of the cone = 1/3 π(2)²(2) = 8π/3 cm³

Find the volume of the toy:

Volume = 16π/3 + 8π/3 = 25.14 cm³

Find the surface area of the hemisphere:

Surface area =  2πr²

Surface area =   2π(2)² = 8π cm²

Find the slanted height of the cone:

a² + b² = c²

2² + 2² = c²

c² = 8

c = √8

c = 2√2

Find the lateral surface area of the cone:

Surface area = πrl

Surface area = π(2)(2√2)

Surface area = 4π√2 cm²

Find the surface area of the cone:

Surface area =  8π  + 4π√2  = 42.92 cm²

Answer: Volume = 25.14 cm³ and Surface area = 42.92 cm²