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Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere3 Marks
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 $[\pi = 3.14]$
✓

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
$=\frac{88000}{21} \div \frac{1100}{21}$
$=\frac{88000}{21} \times \frac{21}{1100}$
$=80$

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