Question
The total area of a solid metallic sphere is $1256 cm^2$. It is melted and recast into solid right circular cones of radius $2.5 cm$ and height $8 cm$. Calculate: the number of cones recasted [π = 3.14]
✓
Answer
$ \therefore r=10 $
Volume of sphere $=\frac{4}{3} \pi r^3=\frac{4}{3} \times \frac{22}{7} \times 10 \times 10 \times 10=\frac{88000}{21} cm ^3$
volume of right circular cone $=$
$ \frac{1}{3} \pi r^2 h=\frac{1}{3} \times \frac{22}{7} \times(2.5)^2 \times 8=\frac{1100}{21} cm ^3 $
Number of cones
$=\frac{88000}{21} \div \frac{1100}{21} $
$=\frac{88000}{21} \times \frac{21}{1100} $
$ =80$
Volume of sphere $=\frac{4}{3} \pi r^3=\frac{4}{3} \times \frac{22}{7} \times 10 \times 10 \times 10=\frac{88000}{21} cm ^3$
volume of right circular cone $=$
$ \frac{1}{3} \pi r^2 h=\frac{1}{3} \times \frac{22}{7} \times(2.5)^2 \times 8=\frac{1100}{21} cm ^3 $
Number of cones
$=\frac{88000}{21} \div \frac{1100}{21} $
$=\frac{88000}{21} \times \frac{21}{1100} $
$ =80$
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