A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 7 cm and height 3 cm. find the number of cones so formed.
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Answered by
11
Volume of sphere=n×volume of cone
22/7×21/2×21/2×21/2×4/3=1/3×22/7×49/4×3×n
9×21×2=3×n
n=21×6=126 cones
126 cones can be formed
22/7×21/2×21/2×21/2×4/3=1/3×22/7×49/4×3×n
9×21×2=3×n
n=21×6=126 cones
126 cones can be formed
Answered by
6
diameter of metallic sphere = 21cm
radius = 21 ÷ 2 = 10.5cm
volume = 4πr^3/ 3
= 4×22×(10.5)^3/ 7×3 = 4851cm^3
diameter of cone = 7cm ,
radius = 7 ÷ 2 = 3.5 cm
height = 3cm
volume = πr^2h/ 3
22(3.5)^2 × 3/ 7 ×3
= 115.5
number of cones so formed
= 4851/ 115.5= 42
Answer: number of cones formed = 42
radius = 21 ÷ 2 = 10.5cm
volume = 4πr^3/ 3
= 4×22×(10.5)^3/ 7×3 = 4851cm^3
diameter of cone = 7cm ,
radius = 7 ÷ 2 = 3.5 cm
height = 3cm
volume = πr^2h/ 3
22(3.5)^2 × 3/ 7 ×3
= 115.5
number of cones so formed
= 4851/ 115.5= 42
Answer: number of cones formed = 42
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