A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 4 2/3 cm and height 3cm. Find the number of cones so formed.
Answers
Answer:
672
Step-by-step explanation:
Diameter of the sphere = 28 cm
Thus, radius of the sphere = 28/2 = 14 cm
Diameter of cone = 14/3 cm
Thus, radius of the cone = 14/3 / 2
radius of cone = 7/3
Volume of the sphere = 4/3πr³
Volume of cone = 1/3πr²h
Number of cones = Volume of sphere/Volume of cone
= (4/3 × 14 × 14 × 14)/(1/3 × 7/3 × 7/3 × 3)
= 10976 × 9/147
= 672
Therefore, the number of cones so formed is 672.
Answer:
Step-by-step explanation:
Diameter of the sphere = 28 cm
Thus, radius of the sphere = 28/2 = 14 cm
Diameter of cone = 14/3 cm
Thus, radius of the cone = 14/3 / 2
radius of cone = 7/3
Volume of the sphere = 4/3πr³
Volume of cone = 1/3πr²h
Number of cones = Volume of sphere/Volume of cone
= (4/3 × 14 × 14 × 14)/(1/3 × 7/3 × 7/3 × 3)
= 10976 × 9/147
= 672
Therefore, the number of cones so formed is 672.