The surface area of a solid sphere is 1256cm². It is melted and recast into cones of radius 2.5cm and height 8cm. Find :i) The radius of the sphere.ii) Number of cones recast. Take π = 3.14.
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Answer:
(i) 10 cm (ii) 80 cones
Step-by-step explanation:
Surface area = 1256 cm²
Find the radius:
Surface area = 4πr²
4πr² = 1256
r² = 1256 ÷ 4π
r² = 100
r = √100
r = 10 cm
Find the volume of the sphere:
Volume = 4/3 πr³
Volume = 4/3 π(10)³
Volume = 4000π/3 cm³
Find the volume of a cone:
Volume = 1/3 πr²h
Volume = 1/3 π(2.5)²(8) = 50π/3 cm³
Find the number of cones recast:
Number of cones = 4000π/3 ÷ 50π/3
Number of cones = 80
Answer: (i) 10 cm (ii) 80 cones
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