ICSE Class X Math 2013 Solved Paper

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Question : 33
Total: 46
A solid sphere of radius 15‌cm is melted and recast into solid right circular cones of radius 2.5‌cm and height 8‌cm . Calculate the number of cones recast.
Solution:  
Radius of a solid sphere, r=15‌cm
‌ Volume of a solid sphere ‌‌=‌
4
3
Ï€
r3

‌=‌
4
3
×π(15)3cm3
.

Now, radius of right circular cone =2.5‌cm and ‌ height, ‌h=8‌cm‌. ‌
Volume of right circular cone =‌
1
3
Ï€
r2
h

=‌
1
3
Ï€
(2.5)2
×8

∴ The number of cones =‌
‌ Volume of a sphere ‌
‌ Volume of a cone ‌

‌=‌
‌
4
3
Ï€
×(15)3
1
3
Ï€
(2.5)2
×8

‌=‌
15×15×15
2.5×2.5×2

‌=270
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