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Cylinder, Cone and Sphere — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCylinder, Cone and Sphere3 Marks
Question
The surface area of a solid metallic sphere is $2464 cm^2.$ It is melted and recast into solid right circular cones of radius $3.5 cm$ and height $7 cm.$ Calculate : the number of cones recast. $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
✓

Answer

$\therefore R = 14 cm$
Volume of sphere melted = $\frac{4}{3} \pi R ^3$
$=\frac{4}{3} \times \pi \times 14 \times 14 \times 14$
Radius of each cone recasted $= r = 3.5 cm$
Height of each cone recasted $= h = 7 cm$
$\therefore$ Volume of each cone recasted $=\frac{1}{3} \pi r ^2 h$
$=\frac{1}{3} \times \pi \times 3.5 \times 3.5 \times 7$
$\therefore$ Number of cones recasted $=\frac{\text { Volume of sphere melted }}{\text { Volume of each cone formed }}$
$=\frac{\frac{4}{3} \times \pi \times 14 \times 14 \times 14}{\frac{1}{3} \times \pi \times 3.5 \times 3.5 \times 7}$
$=128$

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