A metallic sphere with a radius of 35 cm is melted and subsequently transformed into several small solid cones, each having a diameter of 14 cm and a height of 4 cm. How many cones are formed as a result of this process?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 875.
Volume of sphere = × π × r3 = × × 35 × 35 × 35
35 × 35 × 35 = 42875
Volume of sphere = × × 42875 = 4 × 22 × 42875 ÷ 21 = 3773000 ÷ 21 = 179666.67 cm3
Radius of cone = 14 ÷ 2 = 7 cm
Volume of one cone = × π × r² × h = × × 7 × 7 × 4 = 22 × 196 ÷ 21 = 4312 ÷ 21 = 205.33 cm3
Number of cones = Volume of sphere ÷ Volume of one cone = 179666.67 ÷ 205.33 ≈ 875