Question

a solid toy in the form of a right circular cylinder with a hemispherical shape at one end a cone at the other end . their common daimeter is 4.2 and the height of the cylinder and concial position is 12 cm and 7 cm respectively . find the volume of the solid toy

Answer 1

Solution :-

Height of the conical portion = 7 cm and height of the cylindrical portion = 12 cm

Radius = Diameter/2

= 4.2/2

= 2.1 cm

Volume of the solid toy = Volume of the conical portion + Volume of the cylindrical portion + Volume of the hemispherical portion

⇒1/3πr²h + πr²h + 2/3πr³

⇒ (1/3*22/7*2.1*2.1*7) + (22/7*2.1*2.1*12) + 2/3*22/7*2.1*2.1*2.1

⇒ 679.14/21 + 1164.24/7 + 407.484/21 

⇒ (32.14 cu cm) + (166.32 cu cm) + (19.404 cu cm)

⇒ 217.864 cu cm

Answer.

Answer 2

given
height of conical portion = 7 cm
height of cylindrical portion = 12 cm
Radius = d/2 = 4.2/2 = 2.1 cm

===>volume of solid toy = volume of conical portion + volume of cylindrical portion + volume of hemispherical portion

===>1/3πr2h + πr2h + 2/3πr3
(1/3 × 22/7 × 2.1 × 2.1 × 7) + (22/7 × 2.1 × 2.1 × 12) + (2/3 × 22/7 × 2.1 × 2.1 × 2.1)

===>(1/3 × 22 × 0.3 × 2.1 × 7) + (22 × 0.3 × 2.1 × 12) + (2/3 × 22 × 0.3 × 2.1 × 2.1)

===>(32.34) + (166.32) + (19.404)

===>218.064 cm

The Volume of the solid toy is 218.064 cm