A solid toy is the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their diameter is 4.2 cm and the heights cylindrical and conical portions are 12 cm and 7 cm respectively.Find the volume of the toy.
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FIGURE IS IN THE ATTACHMENT.
SOLUTION:
GIVEN:
Height of the conical portion (h1)= 7 cm
height of the cylindrical portion (h2)= 12 cm
Diameter of Cylinder, cone & hemisphere= 4.2 cm
Radius of Cylinder, cone & hemisphere(r)= 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
Volume of the solid toy = 1/3πr²h1 + πr²h2 + 2/3πr³
Volume of the solid toy = 1/3πr²[h1 + 3×h2 +2r ]
Volume of the solid toy =1/3×π ×(2.1)² [7 +3×12 + 2× 2.1]
= 1/3×π ×( 2.1)² [7 + 36 + 4.2]
= 1/3×π×( 2.1)²[43+ 4.2]
= 1/3×π×( 2.1)²[47.2]
= (⅓) × (22/7) × 2.1 × 2.1 × 47.2
= 22 × 0.7 × 0.3 × 47.2
= 218.064 cm³
Hence, the volume of the solid toy = 218.064 cm³.
HOPE THIS WILL HELP YOU...
SOLUTION:
GIVEN:
Height of the conical portion (h1)= 7 cm
height of the cylindrical portion (h2)= 12 cm
Diameter of Cylinder, cone & hemisphere= 4.2 cm
Radius of Cylinder, cone & hemisphere(r)= 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
Volume of the solid toy = 1/3πr²h1 + πr²h2 + 2/3πr³
Volume of the solid toy = 1/3πr²[h1 + 3×h2 +2r ]
Volume of the solid toy =1/3×π ×(2.1)² [7 +3×12 + 2× 2.1]
= 1/3×π ×( 2.1)² [7 + 36 + 4.2]
= 1/3×π×( 2.1)²[43+ 4.2]
= 1/3×π×( 2.1)²[47.2]
= (⅓) × (22/7) × 2.1 × 2.1 × 47.2
= 22 × 0.7 × 0.3 × 47.2
= 218.064 cm³
Hence, the volume of the solid toy = 218.064 cm³.
HOPE THIS WILL HELP YOU...
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abhinav18802:
awesome answer
awesome answer
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