Question

Atoy is in the form of a cone mounted on a hemisphere of the same diameter. The diameter
of the base and the height of the cone are 6 cm and 4 cm respectively. Determine the
surface area of the toy. [use pi = 3.14]​

Answer 1

Answer:

Given :

For cone -

1. Height of the cone = 4cm

2. diameter of the cone = 6cm

3.radius of the cone = \frac{6}{2}

2

6

= 3cm

Slant height of the cone l = √r²+h²

⇒ l = √3²+4²

⇒ l = √9+16

⇒ l = 5

Lateral surface area of the cone = πrl

⇒ 3.14 × 3 × 5

⇒ 3.14 × 15

⇒ 47,10 cm²

For Hemisphere -

1. Diameter of the hemisphere = 6cm

2. Radius of hemisphere = \frac{6}{2}

2

6

= 3cm

Lateral surface area of hemisphere = 2πr²

⇒ 2 × 3.14 × 3²

⇒ 2 × 3.14 × 9

⇒ 18 × 3.14

⇒ 56.52 cm²

The surface are of toy = lateral surface area of cone + lateral surface area of hemisphere

⇒ 47.10 + 56.52

⇒ 103.62cm³

∴ The total surface area of toy = 103.62cm³

Answer 2

Answer:

Given :

For cone -

1. Height of the cone = 4cm

2. diameter of the cone = 6cm

3.radius of the cone = = 3cm

Slant height of the cone l = √r²+h²

⇒ l = √3²+4²

⇒ l = √9+16

⇒ l = 5

Lateral surface area of the cone = πrl

⇒ 3.14 × 3 × 5

⇒ 3.14 × 15

⇒ 47,10 cm²

For Hemisphere -

1. Diameter of the hemisphere = 6cm

2. Radius of hemisphere = = 3cm

Lateral surface area of hemisphere = 2πr²

⇒ 2 × 3.14 × 3²

⇒ 2 × 3.14 × 9

⇒ 18 × 3.14

⇒ 56.52 cm²

The surface are of toy = lateral surface area of cone + lateral surface area of hemisphere

⇒ 47.10 + 56.52

⇒ 103.62cm³

∴ The total surface area of toy = 103.62cm³