Question

$\huge \mathfrak \purple{Question}$​

Answer 1

Answer:

Diameter of hemisphere = 14cm

r = 14

r = 7cm

CSA of hemisphere = 2tr²

= 2x4x7x7

= 44 x 7 =

= 308cm²

r = 7cm

h (total) 13cm, h (cylinder) = 13 radiusof hemisphere- 13-7-6cm.

CSA of Cylinder,

= 2ærh

= 2x²x7x6

= 44 x 6

= 264cm²

Surface area of the vessel = CSA of Hemisphere + CSA of Cyclinder

= 308 +264

= 572cm²

Answer 2

Step-by-step explanation:

(1) Diameter = 14 cm, radius = d/2 = 14/2 = 7 cm

Height of the cylindrical portion is 6cm (13-7)

Area of a Curved surface of cylindrical portion = 2πrh

Substitute the values,

= 2 × 22/7 ×7 × 6

= 264 cm²

Area of a curved of hemispherical portion = 2πr²

Substitute the values,

= 2 × 22/7 × 7 × 7

= 308 cm²

Hence, the total surface area is (308 + 264) 572cm².

(2) Total surface area of the toy = Curved surface area of the hemisphere + Curved surface area of the cone

Now,

Curved surface area of the hemisphere = 2πr² and Curved surface area of the cone = πrl

Where 'r' is the radius and 'l' is the slant height.

Radius of the hemisphere (r) = 3.5 cm

Height of the hemisphere is equal to the radius of the hemisphere i.e. 3.5 cm. Radius of the cone is also 3.5 cm.

Now,

Height of the cone = Total height of toy - height of hemisphere

= 15.5 cm - 3.5 cm

= 12 cm

Slant height of the cone (l) = √(r² + h²)

= √[(3.5 cm)² + (12 cm)²]

= √(12.25 + 144) cm²

= √ 56.25 cm²

= 12.5 cm

Total surface area of the toy = curved surface area of the hemisphere + curved surface area of the cone

= 2πr² + πrl

= πr (2r + l)

= 22/7 × 3.5 × (2 × 3.5 + 12.5)

= 22/7 × 3.5 × (7 + 12.5)

= 11 × 19.5

= 214.5

Hence, the total surface area of the toy is 214.5 cm².